The Art Of Doing Algebraic Geometry

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The Art of Doing Algebraic Geometry

Thomas Dedieu,Flaminio Flamini,Claudio Fontanari,Concettina Galati,Rita Pardini
The Art of Doing Algebraic Geometry Book PDF

Author : Thomas Dedieu,Flaminio Flamini,Claudio Fontanari,Concettina Galati,Rita Pardini
Publisher : Springer Nature
Page : 421 pages
File Size : 49,8 Mb
Release : 2023-04-14
Category : Mathematics
ISBN : 9783031119385

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The Art of Doing Algebraic Geometry by Thomas Dedieu,Flaminio Flamini,Claudio Fontanari,Concettina Galati,Rita Pardini Pdf

This volume is dedicated to Ciro Ciliberto on the occasion of his 70th birthday and contains refereed papers, offering an overview of important parts of current research in algebraic geometry and related research in the history of mathematics. It presents original research as well as surveys, both providing a valuable overview of the current state of the art of the covered topics and reflecting the versatility of the scientific interests of Ciro Ciliberto.

Current Developments in Algebraic Geometry

Lucia Caporaso
Current Developments in Algebraic Geometry Book PDF

Author : Lucia Caporaso
Publisher : Cambridge University Press
Page : 437 pages
File Size : 46,8 Mb
Release : 2012-03-19
Category : Mathematics
ISBN : 9780521768252

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Current Developments in Algebraic Geometry by Lucia Caporaso Pdf

This volume, based on a workshop by the MSRI, offers an overview of the state of the art in many areas of algebraic geometry.

Foundations of Algebraic Geometry. --; 29

André 1906- Weil
Foundations of Algebraic Geometry 29 Book PDF

Author : André 1906- Weil
Publisher : Hassell Street Press
Page : 392 pages
File Size : 48,9 Mb
Release : 2021-09-10
Category : Electronic
ISBN : 1015107672

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Foundations of Algebraic Geometry. --; 29 by André 1906- Weil Pdf

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Arithmetic Algebraic Geometry

G., van der Geer,F. Oort,J.H.M. Steenbrink
Arithmetic Algebraic Geometry Book PDF

Author : G., van der Geer,F. Oort,J.H.M. Steenbrink
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 50,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461204572

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Arithmetic Algebraic Geometry by G., van der Geer,F. Oort,J.H.M. Steenbrink Pdf

Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Representative of these recent developments is the notion of Arakelov geometry, a way of "completing" a variety over the ring of integers of a number field by adding fibres over the Archimedean places. Another is the appearance of the relations between arithmetic geometry and Nevanlinna theory, or more precisely between diophantine approximation theory and the value distribution theory of holomorphic maps. Research mathematicians and graduate students in algebraic geometry and number theory will find a valuable and lively view of the field in this state-of-the-art selection.

Advances in Algebraic Geometry Motivated by Physics

Emma Previato
Advances in Algebraic Geometry Motivated by Physics Book PDF

Author : Emma Previato
Publisher : American Mathematical Soc.
Page : 310 pages
File Size : 42,8 Mb
Release : 2001
Category : Geometry, Algebraic
ISBN : 9780821828106

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Advances in Algebraic Geometry Motivated by Physics by Emma Previato Pdf

Our knowledge of objects of algebraic geometry such as moduli of curves, (real) Schubert classes, fundamental groups of complements of hyperplane arrangements, toric varieties, and variation of Hodge structures, has been enhanced recently by ideas and constructions of quantum field theory, such as mirror symmetry, Gromov-Witten invariants, quantum cohomology, and gravitational descendants. These are some of the themes of this refereed collection of papers, which grew out of the special session, ``Enumerative Geometry in Physics,'' held at the AMS meeting in Lowell, MA, April 2000. This session brought together mathematicians and physicists who reported on the latest results and open questions; all the abstracts are included as an Appendix, and also included are papers by some who could not attend. The collection provides an overview of state-of-the-art tools, links that connect classical and modern problems, and the latest knowledge available.

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 : 41,5 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.

Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory

Gebhard Böckle,Wolfram Decker,Gunter Malle
Algorithmic and Experimental Methods in Algebra Geometry and Number Theory Book PDF

Author : Gebhard Böckle,Wolfram Decker,Gunter Malle
Publisher : Springer
Page : 753 pages
File Size : 51,9 Mb
Release : 2018-03-22
Category : Mathematics
ISBN : 9783319705668

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Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory by Gebhard Böckle,Wolfram Decker,Gunter Malle Pdf

This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.

Algebraic Geometry I

V.I. Danilov,V.V. Shokurov
Algebraic Geometry I Book PDF

Author : V.I. Danilov,V.V. Shokurov
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 43,9 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9783642578786

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Algebraic Geometry I by V.I. Danilov,V.V. Shokurov Pdf

"... To sum up, this book helps to learn algebraic geometry in a short time, its concrete style is enjoyable for students and reveals the beauty of mathematics." --Acta Scientiarum Mathematicarum

Koszul Cohomology and Algebraic Geometry

Marian Aprodu,Jan Nagel
Koszul Cohomology and Algebraic Geometry Book PDF

Author : Marian Aprodu,Jan Nagel
Publisher : American Mathematical Soc.
Page : 138 pages
File Size : 50,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849644

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Koszul Cohomology and Algebraic Geometry by Marian Aprodu,Jan Nagel Pdf

The systematic use of Koszul cohomology computations in algebraic geometry can be traced back to the foundational work of Mark Green in the 1980s. Green connected classical results concerning the ideal of a projective variety with vanishing theorems for Koszul cohomology. Green and Lazarsfeld also stated two conjectures that relate the Koszul cohomology of algebraic curves with the existence of special divisors on the curve. These conjectures became an important guideline for future research. In the intervening years, there has been a growing interaction between Koszul cohomology and algebraic geometry. Green and Voisin applied Koszul cohomology to a number of Hodge-theoretic problems, with remarkable success. More recently, Voisin achieved a breakthrough by proving Green's conjecture for general curves; soon afterwards, the Green-Lazarsfeld conjecture for general curves was proved as well. This book is primarily concerned with applications of Koszul cohomology to algebraic geometry, with an emphasis on syzygies of complex projective curves. The authors' main goal is to present Voisin's proof of the generic Green conjecture, and subsequent refinements. They discuss the geometric aspects of the theory and a number of concrete applications of Koszul cohomology to problems in algebraic geometry, including applications to Hodge theory and to the geometry of the moduli space of curves.

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.

Algebraic Geometry and Singularities

Antonio Campillo Lopez,Luis Narvaez Macarro
Algebraic Geometry and Singularities Book PDF

Author : Antonio Campillo Lopez,Luis Narvaez Macarro
Publisher : Birkhäuser
Page : 418 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034890205

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Algebraic Geometry and Singularities by Antonio Campillo Lopez,Luis Narvaez Macarro Pdf

The focus of this volume lies on singularity theory in algebraic geometry. It includes papers documenting recent and original developments and methods in subjects such as resolution of singularities, D-module theory, singularities of maps and geometry of curves. The papers originate from the Third International Conference on Algebraic Geometry held in La Rbida, Spain, in December 1991. Since then, the articles have undergone a meticulous process of refereeing and improvement, and they have been organized into a comprehensive account of the state of the art in this field.

An Algebraic Geometric Approach to Separation of Variables

Konrad Schöbel
An Algebraic Geometric Approach to Separation of Variables Book PDF

Author : Konrad Schöbel
Publisher : Springer
Page : 138 pages
File Size : 47,6 Mb
Release : 2015-10-15
Category : Science
ISBN : 9783658114084

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An Algebraic Geometric Approach to Separation of Variables by Konrad Schöbel Pdf

Konrad Schöbel aims to lay the foundations for a consequent algebraic geometric treatment of variable Separation, which is one of the oldest and most powerful methods to construct exact solutions for the fundamental equations in classical and quantum physics. The present work reveals a surprising algebraic geometric structure behind the famous list of separation coordinates, bringing together a great range of mathematics and mathematical physics, from the late 19th century theory of separation of variables to modern moduli space theory, Stasheff polytopes and operads. "I am particularly impressed by his mastery of a variety of techniques and his ability to show clearly how they interact to produce his results.” (Jim Stasheff)

Geometry of Higher Dimensional Algebraic Varieties

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

Author : Yoichi Miyaoka,Thomas Peternell
Publisher : Birkhauser
Page : 232 pages
File Size : 50,5 Mb
Release : 1997
Category : Mathematics
ISBN : UOM:39015040542055

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

The subject of this book is the classification theory and geometry of higher dimensional varieties: existence and geometry of rational curves via characteristic p-methods, manifolds with negative Kodaira dimension, vanishing theorems, theory of extremal rays (Mori theory), and minimal models. The book gives a state-of-the-art introduction to a difficult and not readily accessible subject which has undergone enormous development in the last two decades. With no loss of precision, the volume focuses on the spread of ideas rather than on a deliberate inclusion of all proofs. The methods presented vary from complex analysis to complex algebraic geometry and algebraic geometry over fields of positive characteristics. The intended audience includes students in algebraic geometry and analysis as well as researchers in these fields and experts from other areas who wish to gain an overview of the theory.

Algebraic Geometry

Robin Hartshorne
Algebraic Geometry Book PDF

Author : Robin Hartshorne
Publisher : Springer Science & Business Media
Page : 511 pages
File Size : 53,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475738490

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Algebraic Geometry by Robin Hartshorne Pdf

An introduction to abstract algebraic geometry, with the only prerequisites being results from commutative algebra, which are stated as needed, and some elementary topology. More than 400 exercises distributed throughout the book offer specific examples as well as more specialised topics not treated in the main text, while three appendices present brief accounts of some areas of current research. This book can thus be used as textbook for an introductory course in algebraic geometry following a basic graduate course in algebra. Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. He is the author of "Residues and Duality", "Foundations of Projective Geometry", "Ample Subvarieties of Algebraic Varieties", and numerous research titles.

Recent Developments in Algebraic Geometry

Hamid Abban,Gavin Brown,Alexander Kasprzyk,Shigefumi Mori
Recent Developments in Algebraic Geometry Book PDF

Author : Hamid Abban,Gavin Brown,Alexander Kasprzyk,Shigefumi Mori
Publisher : Cambridge University Press
Page : 368 pages
File Size : 53,8 Mb
Release : 2022-09-30
Category : Mathematics
ISBN : 9781009190824

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Recent Developments in Algebraic Geometry by Hamid Abban,Gavin Brown,Alexander Kasprzyk,Shigefumi Mori Pdf

Written in celebration of Miles Reid's 70th birthday, this illuminating volume contains 11 papers by leading mathematicians in and around algebraic geometry, broadly related to the themes and interests of Reid's varied career. Just as in Reid's own scientific output, some of the papers give comprehensive accounts of the state of the art of foundational matters, while others give expositions of subject areas or techniques in concrete terms. Reid has been one of the major expositors of algebraic geometry and a great influence on many in this field – this book hopes to inspire a new generation of graduate students and researchers in his tradition.