Algebraic Varieties PDF Download
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Author: G. Kempf
Publisher: Cambridge University Press
ISBN: 9780521426138
Category : Mathematics
Languages : en
Pages : 180
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Book Description
An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.
Author: G. Kempf
Publisher: Cambridge University Press
ISBN: 9780521426138
Category : Mathematics
Languages : en
Pages : 180
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Book Description
An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.
Author: Robin Hartshorne
Publisher: Springer
ISBN: 3540363459
Category : Mathematics
Languages : en
Pages : 271
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Book Description
Author: Brian Osserman
Publisher: American Mathematical Society
ISBN: 1470466651
Category : Mathematics
Languages : en
Pages : 259
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Book Description
Author: Janos Kollar
Publisher: Springer Science & Business Media
ISBN: 3662032767
Category : Mathematics
Languages : en
Pages : 330
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Book Description
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: Frédéric Mangolte
Publisher: Springer Nature
ISBN: 3030431045
Category : Mathematics
Languages : en
Pages : 453
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Book Description
This book gives a systematic presentation of real algebraic varieties. Real algebraic varieties are ubiquitous.They are the first objects encountered when learning of coordinates, then equations, but the systematic study of these objects, however elementary they may be, is formidable. This book is intended for two kinds of audiences: it accompanies the reader, familiar with algebra and geometry at the masters level, in learning the basics of this rich theory, as much as it brings to the most advanced reader many fundamental results often missing from the available literature, the “folklore”. In particular, the introduction of topological methods of the theory to non-specialists is one of the original features of the book. The first three chapters introduce the basis and classical methods of real and complex algebraic geometry. The last three chapters each focus on one more specific aspect of real algebraic varieties. A panorama of classical knowledge is presented, as well as major developments of the last twenty years in the topology and geometry of varieties of dimension two and three, without forgetting curves, the central subject of Hilbert's famous sixteenth problem. Various levels of exercises are given, and the solutions of many of them are provided at the end of each chapter.
Author: Bjorn Poonen
Publisher: Springer Science & Business Media
ISBN: 0817681701
Category : Mathematics
Languages : en
Pages : 292
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Book Description
This text offers a collection of survey and research papers by leading specialists in the field documenting the current understanding of higher dimensional varieties. Recently, it has become clear that ideas from many branches of mathematics can be successfully employed in the study of rational and integral points. This book will be very valuable for researchers from these various fields who have an interest in arithmetic applications, specialists in arithmetic geometry itself, and graduate students wishing to pursue research in this area.
Author: Thomas Peternell
Publisher: Birkhäuser
ISBN: 3034888937
Category : Mathematics
Languages : en
Pages : 221
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Book Description
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.
Author: Christopher D. Hacon
Publisher: Springer Science & Business Media
ISBN: 3034602901
Category : Mathematics
Languages : en
Pages : 206
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Book Description
Higher Dimensional Algebraic Geometry presents recent advances in the classification of complex projective varieties. Recent results in the minimal model program are discussed, and an introduction to the theory of moduli spaces is presented.
Author: Piotr Pragacz
Publisher: Springer Science & Business Media
ISBN: 3764373423
Category : Mathematics
Languages : en
Pages : 321
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Book Description
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: Kang Zuo
Publisher: Springer
ISBN: 3540484248
Category : Mathematics
Languages : en
Pages : 142
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Book Description
Using harmonic maps, non-linear PDE and techniques from algebraic geometry this book enables the reader to study the relation between fundamental groups and algebraic geometry invariants of algebraic varieties. The reader should have a basic knowledge of algebraic geometry and non-linear analysis. This book can form the basis for graduate level seminars in the area of topology of algebraic varieties. It also contains present new techniques for researchers working in this area.
