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 | : 176 |
| 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 | : Michel Zouboulakis |
| Publisher | : Routledge |
| Total Pages | : 188 |
| Release | : 2014-01-21 |
| Genre | : Business & Economics |
| ISBN | : 1317817494 |
Download The Varieties of Economic Rationality Book in PDF, ePub and Kindle
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 .
| Author | : Emmanuel Peyre |
| Publisher | : Birkhäuser |
| Total Pages | : 455 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3034883684 |
Download Rational Points on Algebraic Varieties Book in PDF, ePub and Kindle
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.
| 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 | : Olivier Debarre |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 245 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 147575406X |
Download Higher-Dimensional Algebraic Geometry Book in PDF, ePub and Kindle
The classification theory of algebraic varieties is the focus of this book. This very active area of research is still developing, but an amazing quantity of knowledge has accumulated over the past twenty years. The authors goal is to provide an easily accessible introduction to the subject. The book starts with preparatory and standard definitions and results, then moves on to discuss various aspects of the geometry of smooth projective varieties with many rational curves, and finishes in taking the first steps towards Moris minimal model program of classification of algebraic varieties by proving the cone and contraction theorems. The book is well-organized and the author has kept the number of concepts that are used but not proved to a minimum to provide a mostly self-contained introduction.
| Author | : Shiing-Shen Chern |
| Publisher | : World Scientific |
| Total Pages | : 522 |
| Release | : 2002 |
| Genre | : Mathematics |
| ISBN | : 9812776923 |
Download The Collected Papers of Wei-Liang Chow Book in PDF, ePub and Kindle
This invaluable book contains the collected papers of Prof Wei-Liang Chow, an original and versatile mathematician of the 20th Century. Prof Chow''s name has become a household word in mathematics because of the Chow ring, Chow coordinates, and Chow''s theorem on analytic sets in projective spaces. The Chow ring has many advantages and is widely used in intersection theory of algebraic geometry. Chow coordinates have been a very versatile tool in many aspects of algebraic geometry. Chow''s theorem OCo that a compact analytic variety in a projective space is algebraic OCo is justly famous; it shows the close analogy between algebraic geometry and algebraic number theory.About Professor Wei-Liang ChowThe long and distinguished career of Prof Wei-Liang Chow (1911OCo95) as a mathematician began in China with professorships at the National Central University in Nanking (1936OCo37) and the National Tung-Chi University in Shanghai (1946OCo47), and ultimately led him to the United States, where he joined the mathematics faculty of Johns Hopkins University in Baltimore, Maryland, first as an associate professor from 1948 to 1950, then as a full professor from 1950 until his retirement in 1977.In addition to serving as chairman of the mathematics department at Johns Hopkins from 1955 to 1965, he was Editor-in-Chief of the American Journal of Mathematics from 1953 to 1977."
