Rationality Of Varieties

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Rationality of Varieties

Gavril Farkas,Gerard van der Geer,Mingmin Shen,Lenny Taelman
Rationality of Varieties Book PDF

Author : Gavril Farkas,Gerard van der Geer,Mingmin Shen,Lenny Taelman
Publisher : Springer Nature
Page : 433 pages
File Size : 52,9 Mb
Release : 2021-10-19
Category : Mathematics
ISBN : 9783030754211

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Rationality of Varieties by Gavril Farkas,Gerard van der Geer,Mingmin Shen,Lenny Taelman Pdf

This book provides an overview of the latest progress on rationality questions in algebraic geometry. It discusses new developments such as universal triviality of the Chow group of zero cycles, various aspects of stable birationality, cubic and Fano fourfolds, rationality of moduli spaces and birational invariants of group actions on varieties, contributed by the foremost experts in their fields. The question of whether an algebraic variety can be parametrized by rational functions of as many variables as its dimension has a long history and played an important role in the history of algebraic geometry. Recent developments in algebraic geometry have made this question again a focal point of research and formed the impetus to organize a conference in the series of conferences on the island of Schiermonnikoog. The book follows in the tradition of earlier volumes, which originated from conferences on the islands Texel and Schiermonnikoog.

Rational and Nearly Rational Varieties

János Kollár,Karen E. Smith,Alessio Corti
Rational and Nearly Rational Varieties Book PDF

Author : János Kollár,Karen E. Smith,Alessio Corti
Publisher : Cambridge University Press
Page : 246 pages
File Size : 51,7 Mb
Release : 2004-04-22
Category : Mathematics
ISBN : 0521832071

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Rational and Nearly Rational Varieties by János Kollár,Karen E. Smith,Alessio Corti Pdf

The most basic algebraic varieties are the projective spaces, and rational varieties are their closest relatives. In many applications where algebraic varieties appear in mathematics and the sciences, we see rational ones emerging as the most interesting examples. The authors have given an elementary treatment of rationality questions using a mix of classical and modern methods. Arising from a summer school course taught by János Kollár, this book develops the modern theory of rational and nearly rational varieties at a level that will particularly suit graduate students. There are numerous examples and exercises, all of which are accompanied by fully worked out solutions, that will make this book ideal as the basis of a graduate course. It will act as a valuable reference for researchers whilst helping graduate students to reach the point where they can begin to tackle contemporary research problems.

Rational Curves on Algebraic Varieties

Janos Kollar
Rational Curves on Algebraic Varieties Book PDF

Author : Janos Kollar
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 48,6 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9783662032763

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Rational Curves on Algebraic Varieties by Janos Kollar Pdf

The aim of this book is to provide an introduction to the structure theory of higher dimensional algebraic varieties by studying the geometry of curves, especially rational curves, on varieties. The main applications are in the study of Fano varieties and of related varieties with lots of rational curves on them. This Ergebnisse volume provides the first systematic introduction to this field of study. The book contains a large number of examples and exercises which serve to illustrate the range of the methods and also lead to many open questions of current research.

Rational Points on Varieties

Bjorn Poonen
Rational Points on Varieties Book PDF

Author : Bjorn Poonen
Publisher : American Mathematical Society
Page : 357 pages
File Size : 54,5 Mb
Release : 2023-08-10
Category : Mathematics
ISBN : 9781470474584

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Rational Points on Varieties by Bjorn Poonen Pdf

This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one—this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and descent obstructions. A final chapter applies all these to study the arithmetic of surfaces. The down-to-earth explanations and the over 100 exercises make the book suitable for use as a graduate-level textbook, but even experts will appreciate having a single source covering many aspects of geometry over an unrestricted ground field and containing some material that cannot be found elsewhere. The origins of arithmetic (or Diophantine) geometry can be traced back to antiquity, and it remains a lively and wide research domain up to our days. The book by Bjorn Poonen, a leading expert in the field, opens doors to this vast field for many readers with different experiences and backgrounds. It leads through various algebraic geometric constructions towards its central subject: obstructions to existence of rational points. —Yuri Manin, Max-Planck-Institute, Bonn It is clear that my mathematical life would have been very different if a book like this had been around at the time I was a student. —Hendrik Lenstra, University Leiden Understanding rational points on arbitrary algebraic varieties is the ultimate challenge. We have conjectures but few results. Poonen's book, with its mixture of basic constructions and openings into current research, will attract new generations to the Queen of Mathematics. —Jean-Louis Colliot-Thélène, Université Paris-Sud A beautiful subject, handled by a master. —Joseph Silverman, Brown University

Rationality Problems in Algebraic Geometry

Arnaud Beauville,Brendan Hassett,Alexander Kuznetsov,Alessandro Verra
Rationality Problems in Algebraic Geometry Book PDF

Author : Arnaud Beauville,Brendan Hassett,Alexander Kuznetsov,Alessandro Verra
Publisher : Springer
Page : 170 pages
File Size : 55,8 Mb
Release : 2016-12-06
Category : Mathematics
ISBN : 9783319462097

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Rationality Problems in Algebraic Geometry by Arnaud Beauville,Brendan Hassett,Alexander Kuznetsov,Alessandro Verra Pdf

Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel–Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.

Rationality of Varieties

Gavril Farkas,Gerard van der Geer,Mingmin Shen,Lenny Taelman
Rationality of Varieties Book PDF

Author : Gavril Farkas,Gerard van der Geer,Mingmin Shen,Lenny Taelman
Publisher : Unknown
Page : 0 pages
File Size : 54,5 Mb
Release : 2021
Category : Electronic
ISBN : 3030754227

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Rationality of Varieties by Gavril Farkas,Gerard van der Geer,Mingmin Shen,Lenny Taelman Pdf

This book provides an overview of the latest progress on rationality questions in algebraic geometry. It discusses new developments such as universal triviality of the Chow group of zero cycles, various aspects of stable birationality, cubic and Fano fourfolds, rationality of moduli spaces and birational invariants of group actions on varieties, contributed by the foremost experts in their fields. The question of whether an algebraic variety can be parametrized by rational functions of as many variables as its dimension has a long history and played an important role in the history of algebraic geometry. Recent developments in algebraic geometry have made this question again a focal point of research and formed the impetus to organize a conference in the series of conferences on the island of Schiermonnikoog. The book follows in the tradition of earlier volumes, which originated from conferences on the islands Texel and Schiermonnikoog.

The Varieties of Economic Rationality

Michel Zouboulakis
The Varieties of Economic Rationality Book PDF

Author : Michel Zouboulakis
Publisher : Routledge
Page : 188 pages
File Size : 55,9 Mb
Release : 2014-01-21
Category : Business & Economics
ISBN : 9781317817499

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The Varieties of Economic Rationality by Michel Zouboulakis Pdf

The concept of economic rationality is important for the historical evolution of Economics as a scientific discipline. The common idea about this concept -even between economists- is that it has a unique meaning which is universally accepted. This new volume argues that "economic rationality" is not not a universal concept with one single meaning, and that it in fact has different, if not conflicting, interpretations in the evolution of discourse on economics. In order to achieve this, the book traces the historical evolution of the concept of economic rationality from Adam Smith to the present, taking in thinkers from Mill to Friedman, and encompassing approaches from neoclassical to behavioural economics. The book charts this history in order to reveal important instances of conceptual transformation of the meaning of economic rationality. In doing so, it presents a uniquely detailed study of the historical change of the many faces of the homo oeconomicus .

Rational Points on Algebraic Varieties

Emmanuel Peyre,Yuri Tschinkel
Rational Points on Algebraic Varieties Book PDF

Author : Emmanuel Peyre,Yuri Tschinkel
Publisher : Birkhäuser
Page : 455 pages
File Size : 53,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034883689

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Rational Points on Algebraic Varieties by Emmanuel Peyre,Yuri Tschinkel Pdf

This book is devoted to the study of rational and integral points on higher-dimensional algebraic varieties. It contains carefully selected research papers addressing the arithmetic geometry of varieties which are not of general type, with an emphasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The present volume gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric constructions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups.

Geometry of Higher Dimensional Algebraic Varieties

Thomas Peternell,Joichi Miyaoka
Geometry of Higher Dimensional Algebraic Varieties Book PDF

Author : Thomas Peternell,Joichi Miyaoka
Publisher : Birkhäuser
Page : 221 pages
File Size : 48,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034888936

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Geometry of Higher Dimensional Algebraic Varieties by Thomas Peternell,Joichi Miyaoka Pdf

This book is based on lecture notes of a seminar of the Deutsche Mathematiker Vereinigung held by the authors at Oberwolfach from April 2 to 8, 1995. It gives an introduction to the classification theory and geometry of higher dimensional complex-algebraic varieties, focusing on the tremendeous developments of the sub ject in the last 20 years. The work is in two parts, with each one preceeded by an introduction describing its contents in detail. Here, it will suffice to simply ex plain how the subject matter has been divided. Cum grano salis one might say that Part 1 (Miyaoka) is more concerned with the algebraic methods and Part 2 (Peternell) with the more analytic aspects though they have unavoidable overlaps because there is no clearcut distinction between the two methods. Specifically, Part 1 treats the deformation theory, existence and geometry of rational curves via characteristic p, while Part 2 is principally concerned with vanishing theorems and their geometric applications. Part I Geometry of Rational Curves on Varieties Yoichi Miyaoka RIMS Kyoto University 606-01 Kyoto Japan Introduction: Why Rational Curves? This note is based on a series of lectures given at the Mathematisches Forschungsin stitut at Oberwolfach, Germany, as a part of the DMV seminar "Mori Theory". The construction of minimal models was discussed by T.

Birational Geometry, Rational Curves, and Arithmetic

Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel
Birational Geometry Rational Curves and Arithmetic Book PDF

Author : Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 324 pages
File Size : 48,7 Mb
Release : 2013-05-17
Category : Mathematics
ISBN : 9781461464822

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Birational Geometry, Rational Curves, and Arithmetic by Fedor Bogomolov,Brendan Hassett,Yuri Tschinkel Pdf

​​​​This book features recent developments in a rapidly growing area at the interface of higher-dimensional birational geometry and arithmetic geometry. It focuses on the geometry of spaces of rational curves, with an emphasis on applications to arithmetic questions. Classically, arithmetic is the study of rational or integral solutions of diophantine equations and geometry is the study of lines and conics. From the modern standpoint, arithmetic is the study of rational and integral points on algebraic varieties over nonclosed fields. A major insight of the 20th century was that arithmetic properties of an algebraic variety are tightly linked to the geometry of rational curves on the variety and how they vary in families. This collection of solicited survey and research papers is intended to serve as an introduction for graduate students and researchers interested in entering the field, and as a source of reference for experts working on related problems. Topics that will be addressed include: birational properties such as rationality, unirationality, and rational connectedness, existence of rational curves in prescribed homology classes, cones of rational curves on rationally connected and Calabi-Yau varieties, as well as related questions within the framework of the Minimal Model Program.

Digital Economy: Complexity and Variety vs. Rationality

Elena G. Popkova,Bruno S. Sergi
Digital Economy Complexity and Variety vs Rationality Book PDF

Author : Elena G. Popkova,Bruno S. Sergi
Publisher : Springer Nature
Page : 1055 pages
File Size : 45,7 Mb
Release : 2019-09-14
Category : Technology & Engineering
ISBN : 9783030295868

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Digital Economy: Complexity and Variety vs. Rationality by Elena G. Popkova,Bruno S. Sergi Pdf

This proceedings book features selected papers from the 9th National Scientific and Practical Conference “Digital Economy: Complexity and Variety Vs. Rationality,” which took place on April 17–18, 2019, in Vladimir (Russian Federation). It presents the latest research in the field of the digital economy, discussing its role in the creation of advantages for the state, entrepreneurship, and society, as well as the emergence of new economic risks. The chapters address the following topics: the importance of economy’s digital modernization, tools for the formation of the digital economy in Russia, specific features and perspectives of digital modernization of the regional economy, an overview of the social consequences of transition to the digital economy, financial components of the digital economy, legal challenges regarding the digital reality for society and state, and the main challenges and threats to the profession of jurisprudence in the context of the digitization of the economy. Intended for representatives of the academic community and researchers interested in the formation of the digital economy and digital society as well as undergraduates, postgraduates, and masters of economic specialties, the book is also a valuable resource for companies that use or wishing to implement digital technologies into their economic practices; and public and government employees involved with monitoring, control, and regulation of the digital economy.

Rational Points on Varieties

Bjorn Poonen
Rational Points on Varieties Book PDF

Author : Bjorn Poonen
Publisher : Unknown
Page : 128 pages
File Size : 42,5 Mb
Release : 2017
Category : MATHEMATICS
ISBN : 1470443155

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Rational Points on Varieties by Bjorn Poonen Pdf

This book is motivated by the problem of determining the set of rational points on a variety, but its true goal is to equip readers with a broad range of tools essential for current research in algebraic geometry and number theory. The book is unconventional in that it provides concise accounts of many topics instead of a comprehensive account of just one-this is intentionally designed to bring readers up to speed rapidly. Among the topics included are Brauer groups, faithfully flat descent, algebraic groups, torsors, étale and fppf cohomology, the Weil conjectures, and the Brauer-Manin and de.

Higher Dimensional Varieties and Rational Points

Károly Jr. Böröczky,János Kollár,Szamuely Tamas
Higher Dimensional Varieties and Rational Points Book PDF

Author : Károly Jr. Böröczky,János Kollár,Szamuely Tamas
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 49,9 Mb
Release : 2013-12-11
Category : Mathematics
ISBN : 9783662051238

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Higher Dimensional Varieties and Rational Points by Károly Jr. Böröczky,János Kollár,Szamuely Tamas Pdf

Exploring the connections between arithmetic and geometric properties of algebraic varieties has been the object of much fruitful study for a long time, especially in the case of curves. The aim of the Summer School and Conference on "Higher Dimensional Varieties and Rational Points" held in Budapest, Hungary during September 2001 was to bring together students and experts from the arithmetic and geometric sides of algebraic geometry in order to get a better understanding of the current problems, interactions and advances in higher dimension. The lecture series and conference lectures assembled in this volume give a comprehensive introduction to students and researchers in algebraic geometry and in related fields to the main ideas of this rapidly developing area.

Birational Geometry of Algebraic Varieties

Janos Kollár,Shigefumi Mori
Birational Geometry of Algebraic Varieties Book PDF

Author : Janos Kollár,Shigefumi Mori
Publisher : Cambridge University Press
Page : 264 pages
File Size : 52,9 Mb
Release : 2008-02-04
Category : Mathematics
ISBN : 0521060222

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Birational Geometry of Algebraic Varieties by Janos Kollár,Shigefumi Mori Pdf

One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.

Rational Points on Algebraic Varieties

Emmanuel Peyre,Yuri Tschinkel
Rational Points on Algebraic Varieties Book PDF

Author : Emmanuel Peyre,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 474 pages
File Size : 50,5 Mb
Release : 2001-10-01
Category : Mathematics
ISBN : 3764366125

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Rational Points on Algebraic Varieties by Emmanuel Peyre,Yuri Tschinkel Pdf

This book is devoted to the study of rational and integral points on higher- dimensional algebraic varieties. It contains research papers addressing the arithmetic geometry of varieties which are not of general type, with an em- phasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The book gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric con- structions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups. In recent years there has been substantial progress in our understanding of the arithmetic of algebraic surfaces. Five papers are devoted to cubic surfaces: Basile and Fisher study the existence of rational points on certain diagonal cubics, Swinnerton-Dyer considers weak approximation and Broberg proves upper bounds on the number of rational points on the complement to lines on cubic surfaces. Peyre and Tschinkel compare numerical data with conjectures concerning asymptotics of rational points of bounded height on diagonal cubics of rank 2. Kanevsky and Manin investigate the composition of points on cubic surfaces. Satge constructs rational curves on certain Kummer surfaces. Colliot-Thelene studies the Hasse principle for pencils of curves of genus 1. In an appendix to this paper Skorobogatov produces explicit examples of Enriques surfaces with a Zariski dense set of rational points.