Topics In Cohomological Studies Of Algebraic Varieties

Author : Piotr Pragacz
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 50,8 Mb
Release : 2006-03-30
Category : Mathematics
ISBN : 9783764373429

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Topics in Cohomological Studies of Algebraic Varieties by Piotr Pragacz Pdf

The articles in this volume study various cohomological aspects of algebraic varieties: - characteristic classes of singular varieties; - geometry of flag varieties; - cohomological computations for homogeneous spaces; - K-theory of algebraic varieties; - quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before. Contributors: Paolo Aluffi Michel Brion Anders Skovsted Buch Haibao Duan Ali Ulas Ozgur Kisisel Piotr Pragacz Jörg Schürmann Marek Szyjewski Harry Tamvakis

Author : Piotr Pragacz
Publisher : Unknown
Page : 297 pages
File Size : 45,6 Mb
Release : 2005
Category : Algebra, Homological
ISBN : 0817672141

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Topics in Cohomological Studies of Algebraic Varieties by Piotr Pragacz Pdf

The articles in this volume study various cohomological aspects of algebraic varieties:- characteristic classes of singular varieties;- geometry of flag varieties;- cohomological computations for homogeneous spaces;- K-theory of algebraic varieties;- quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Num.

Author : I.R. Shafarevich
Publisher : Springer Science & Business Media
Page : 270 pages
File Size : 55,5 Mb
Release : 2013-11-22
Category : Mathematics
ISBN : 9783642609251

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Algebraic Geometry II by I.R. Shafarevich Pdf

This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.

Author : Fedor Bogomolov,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 45,8 Mb
Release : 2009-11-03
Category : Mathematics
ISBN : 9780817649340

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Cohomological and Geometric Approaches to Rationality Problems by Fedor Bogomolov,Yuri Tschinkel Pdf

Rationality problems link algebra to geometry, and the difficulties involved depend on the transcendence degree of $K$ over $k$, or geometrically, on the dimension of the variety. A major success in 19th century algebraic geometry was a complete solution of the rationality problem in dimensions one and two over algebraically closed ground fields of characteristic zero. Such advances has led to many interdisciplinary applications to algebraic geometry. This comprehensive book consists of surveys of research papers by leading specialists in the field and gives indications for future research in rationality problems. Topics discussed include the rationality of quotient spaces, cohomological invariants of quasi-simple Lie type groups, rationality of the moduli space of curves, and rational points on algebraic varieties. This volume is intended for researchers, mathematicians, and graduate students interested in algebraic geometry, and specifically in rationality problems. Contributors: F. Bogomolov; T. Petrov; Y. Tschinkel; Ch. Böhning; G. Catanese; I. Cheltsov; J. Park; N. Hoffmann; S. J. Hu; M. C. Kang; L. Katzarkov; Y. Prokhorov; A. Pukhlikov

Author : Brian Osserman
Publisher : American Mathematical Society
Page : 259 pages
File Size : 45,9 Mb
Release : 2021-12-06
Category : Mathematics
ISBN : 9781470466657

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A Concise Introduction to Algebraic Varieties by Brian Osserman Pdf

Author : Piotr Pragacz
Publisher : European Mathematical Society
Page : 520 pages
File Size : 47,8 Mb
Release : 2012
Category : Geometry, Algebraic
ISBN : 3037191147

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Contributions to Algebraic Geometry by Piotr Pragacz Pdf

The articles in this volume are the outcome of the Impanga Conference on Algebraic Geometry in 2010 at the Banach Center in Bedlewo. The following spectrum of topics is covered: K3 surfaces and Enriques surfaces Prym varieties and their moduli invariants of singularities in birational geometry differential forms on singular spaces Minimal Model Program linear systems toric varieties Seshadri and packing constants equivariant cohomology Thom polynomials arithmetic questions The main purpose of the volume is to give comprehensive introductions to the above topics, starting from an elementary level and ending with a discussion of current research. The first four topics are represented by the notes from the mini courses held during the conference. In the articles, the reader will find classical results and methods, as well as modern ones. This book is addressed to researchers and graduate students in algebraic geometry, singularity theory, and algebraic topology. Most of the material in this volume has not yet appeared in book form.

Author : Paolo Aluffi,David Anderson,Milena Hering,Mircea Mustaţă,Sam Payne
Publisher : Cambridge University Press
Page : 417 pages
File Size : 42,8 Mb
Release : 2022-04-07
Category : Mathematics
ISBN : 9781108792509

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Facets of Algebraic Geometry by Paolo Aluffi,David Anderson,Milena Hering,Mircea Mustaţă,Sam Payne Pdf

Written to honor the enduring influence of William Fulton, these articles present substantial contributions to algebraic geometry.

Author : Aldo Conca,Sandra Di Rocco,Jan Draisma,June Huh,Bernd Sturmfels,Filippo Viviani
Publisher : Springer
Page : 245 pages
File Size : 52,6 Mb
Release : 2014-05-15
Category : Mathematics
ISBN : 9783319048703

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Combinatorial Algebraic Geometry by Aldo Conca,Sandra Di Rocco,Jan Draisma,June Huh,Bernd Sturmfels,Filippo Viviani Pdf

Combinatorics and Algebraic Geometry have enjoyed a fruitful interplay since the nineteenth century. Classical interactions include invariant theory, theta functions and enumerative geometry. The aim of this volume is to introduce recent developments in combinatorial algebraic geometry and to approach algebraic geometry with a view towards applications, such as tensor calculus and algebraic statistics. A common theme is the study of algebraic varieties endowed with a rich combinatorial structure. Relevant techniques include polyhedral geometry, free resolutions, multilinear algebra, projective duality and compactifications.

Author : Yves André,Francesco Baldassarri,Maurizio Cailotto
Publisher : Springer Nature
Page : 241 pages
File Size : 44,9 Mb
Release : 2020-07-16
Category : Mathematics
ISBN : 9783030397197

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De Rham Cohomology of Differential Modules on Algebraic Varieties by Yves André,Francesco Baldassarri,Maurizio Cailotto Pdf

"...A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrong...This is a nicely-written book [that] studies algebraic differential modules in several variables." --Mathematical Reviews

Author : I.R. Shafarevich
Publisher : Springer
Page : 264 pages
File Size : 50,7 Mb
Release : 2014-10-05
Category : Mathematics
ISBN : 3642609260

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Algebraic Geometry II by I.R. Shafarevich Pdf

This two-part volume contains numerous examples and insights on various topics. The authors have taken pains to present the material rigorously and coherently. This book will be immensely useful to mathematicians and graduate students working in algebraic geometry, arithmetic algebraic geometry, complex analysis and related fields.

Author : Bjorn Poonen
Publisher : American Mathematical Society
Page : 357 pages
File Size : 55,5 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

Author : V G Gurzadyan,A Klümper,A G Sedrakyan
Publisher : World Scientific
Page : 308 pages
File Size : 51,9 Mb
Release : 2012-11-07
Category : Science
ISBN : 9789814440356

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Low Dimensional Physics and Gauge Principles by V G Gurzadyan,A Klümper,A G Sedrakyan Pdf

This is a collection of articles on fundamental physical principles and methods, the topics ranging from matrix models, random surfaces, quantum dots and rings, to black holes, cosmology and testing of the tiny effects predicted by General Relativity. Among the authors are Sir Roger Penrose and other well-known experts and the articles are addressed to graduate students and researchers. The volume is a Festschrift to a noted physicist and mentor Sergei Matinyan. Contents:A Matrix Model Representation of the Integrable XXZ Heisenberg Chain on Random Surfaces (J Ambjørn and A Sedrakyan)Magnetization and Concurrence Properties of Diamond Chain: Two Approaches (N S Ananikian, H A Lazaryan, M A Nalbandyan, O Rozas and S M de Souza)Non-Trivial Holonomy and Calorons (P van Baal)Spontaneous Breaking of Lorentz-Invariance and Gravitons as Goldstone Particles (Z Berezhiani and O V Kancheli)On Emergent Gauge and Gravity Theories (J L Chkareuli)Geodesic Motion in General Relativity: Lares in Earth's Gravity (I Ciufolini, V G Gurzadyan, R Penrose and A Paolozzi)Collective States of D(D3) Non-Abelian Anyons (P E Finch and H Frahm)Electromagnetic Properties of Neutrinos at an Interface (A N Ioannisian, D A Ioannisian and N A Kazarian)Capture and Ejection of Dark Matter by the Solar System (I B Khriplovich)Topological Theory Of QHE (M Kohmoto)QCD String as an Effective String (Y Makeenko)New Chern–Simons Densities in Both Odd and Even Dimensions (E Radu and T Tchrakian)Photon “Mass” and Atomic Levels in a Superstrong Magnetic Field (M I Vysotsky)Constraints on Parameters of the Black Hole at the Galactic Center (A F Zakharov, F De Paolis, G Ingrosso and A A Nucita)Diffusion in Two-Dimensional Disordered Systems with Particle-Hole Symmetry (K Ziegler)and other papers Readership: Graduate students and researchers in physics. Keywords:Quantum Field Theories;gauge theories;General RelativityKey Features:Up-to-date articles on the modern problems of quantum field theory and General RelativityProminent authorsUnique treatment of mathematical methods and approaches

Author : Hibi Takayuki,Tsuchiya Akiyoshi
Publisher : World Scientific
Page : 476 pages
File Size : 48,8 Mb
Release : 2019-05-30
Category : Mathematics
ISBN : 9789811200496

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Algebraic And Geometric Combinatorics On Lattice Polytopes - Proceedings Of The Summer Workshop On Lattice Polytopes by Hibi Takayuki,Tsuchiya Akiyoshi Pdf

This volume consists of research papers and expository survey articles presented by the invited speakers of the Summer Workshop on Lattice Polytopes. Topics include enumerative, algebraic and geometric combinatorics on lattice polytopes, topological combinatorics, commutative algebra and toric varieties.Readers will find that this volume showcases current trends on lattice polytopes and stimulates further developments of many research areas surrounding this field. With the survey articles, research papers and open problems, this volume provides its fundamental materials for graduate students to learn and researchers to find exciting activities and avenues for further exploration on lattice polytopes.

Author : Farrell Brumley,Maria Paula Gomez Aparicio,Alberto Minguez
Publisher : American Mathematical Soc.
Page : 376 pages
File Size : 50,7 Mb
Release : 2017
Category : Algebraic number theory
ISBN : 9781470435738

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Around Langlands Correspondences by Farrell Brumley,Maria Paula Gomez Aparicio,Alberto Minguez Pdf

This volume contains the proceedings of the international conference ``Around Langlands Correspondences'', held from June 17-20, 2015, at Universite Paris Sud in Orsay, France. The Langlands correspondence (nowadays called the usual Langlands correspondence), conjectured by Robert Langlands in the late 1960s and early 1970s, has recently seen some new mysterious generalizations: the modular Langlands correspondence, the $p$-adic Langlands correspondence, and the geometric Langlands correspondence, the last of which seems to share deep connections with the Baum-Connes conjecture. The aim of this volume is to present, through a mix of research and expository articles, some of the fascinating new directions in number theory and representation theory arising from recent developments in the Langlands program. Special emphasis is placed on nonclassical versions of the conjectural Langlands correspondences, where the underlying field is no longer the complex numbers.

Author : José Luis Cisneros-Molina,Lê Dũng Tráng,José Seade
Publisher : Springer Nature
Page : 822 pages
File Size : 55,8 Mb
Release : 2022-06-06
Category : Mathematics
ISBN : 9783030957605

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Handbook of Geometry and Topology of Singularities III by José Luis Cisneros-Molina,Lê Dũng Tráng,José Seade Pdf

This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariski’s equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom–Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.