Rationality Of Varieties PDF Download
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Author | : Gavril Farkas |
Publisher | : Springer Nature |
Total Pages | : 433 |
Release | : 2021-10-19 |
Genre | : Mathematics |
ISBN | : 3030754219 |
Download Rationality of Varieties Book in PDF, ePub and Kindle
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.
Author | : János Kollár |
Publisher | : Cambridge University Press |
Total Pages | : 246 |
Release | : 2004-04-22 |
Genre | : Mathematics |
ISBN | : 9780521832076 |
Download Rational and Nearly Rational Varieties Book in PDF, ePub and Kindle
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.
Author | : Janos Kollar |
Publisher | : Springer Science & Business Media |
Total Pages | : 330 |
Release | : 2013-04-09 |
Genre | : Mathematics |
ISBN | : 3662032767 |
Download Rational Curves on Algebraic Varieties Book in PDF, ePub and Kindle
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.
Author | : Bjorn Poonen |
Publisher | : American Mathematical Society |
Total Pages | : 357 |
Release | : 2023-08-10 |
Genre | : Mathematics |
ISBN | : 1470474581 |
Download Rational Points on Varieties Book in PDF, ePub and Kindle
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 | : Arnaud Beauville |
Publisher | : Springer |
Total Pages | : 170 |
Release | : 2016-12-06 |
Genre | : Mathematics |
ISBN | : 3319462091 |
Download Rationality Problems in Algebraic Geometry Book in PDF, ePub and Kindle
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.
Author | : Gavril Farkas |
Publisher | : |
Total Pages | : 0 |
Release | : 2021 |
Genre | : |
ISBN | : 9783030754228 |
Download Rationality of Varieties Book in PDF, ePub and Kindle
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.
Author | : M. Hazewinkel |
Publisher | : Springer |
Total Pages | : 932 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1489937919 |
Download Encyclopaedia of Mathematics Book in PDF, ePub and Kindle
Author | : Károly Jr. Böröczky |
Publisher | : Springer Science & Business Media |
Total Pages | : 307 |
Release | : 2013-12-11 |
Genre | : Mathematics |
ISBN | : 3662051230 |
Download Higher Dimensional Varieties and Rational Points Book in PDF, ePub and Kindle
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.
Author | : Bjorn Poonen |
Publisher | : |
Total Pages | : |
Release | : 2017 |
Genre | : MATHEMATICS |
ISBN | : 9781470443153 |
Download Rational Points on Varieties Book in PDF, ePub and Kindle
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.
Author | : Aleksandr V. Pukhlikov |
Publisher | : American Mathematical Soc. |
Total Pages | : 378 |
Release | : 2013-05-15 |
Genre | : Mathematics |
ISBN | : 0821894765 |
Download Birationally Rigid Varieties Book in PDF, ePub and Kindle
Birational rigidity is a striking and mysterious phenomenon in higher-dimensional algebraic geometry. It turns out that certain natural families of algebraic varieties (for example, three-dimensional quartics) belong to the same classification type as the