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Author: G. Kempf
Publisher: Cambridge University Press
Published: 1993-09-09
Total Pages: 180
ISBN-13: 9780521426138
DOWNLOAD EBOOK →An introduction to the theory of algebraic functions on varieties from a sheaf theoretic standpoint.
Author: Robin Hartshorne
Publisher: Springer
Published: 2006-11-15
Total Pages: 271
ISBN-13: 3540363459
DOWNLOAD EBOOK →Author: Janos Kollar
Publisher: Springer Science & Business Media
Published: 2013-04-09
Total Pages: 330
ISBN-13: 3662032767
DOWNLOAD EBOOK →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: Brian Osserman
Publisher: American Mathematical Society
Published: 2021-12-06
Total Pages: 259
ISBN-13: 1470466651
DOWNLOAD EBOOK →Author: Frédéric Mangolte
Publisher: Springer Nature
Published: 2020-09-21
Total Pages: 453
ISBN-13: 3030431045
DOWNLOAD EBOOK →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: Thomas Peternell
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 221
ISBN-13: 3034888937
DOWNLOAD EBOOK →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
Published: 2011-02-02
Total Pages: 220
ISBN-13: 3034602901
DOWNLOAD EBOOK →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: Janos Kollár
Publisher: Cambridge University Press
Published: 2008-02-04
Total Pages: 264
ISBN-13: 9780521060226
DOWNLOAD EBOOK →One of the major discoveries of the past two decades in algebraic geometry is the realization that the theory of minimal models of surfaces can be generalized to higher dimensional varieties. This generalization, called the minimal model program, or Mori's program, has developed into a powerful tool with applications to diverse questions in algebraic geometry and beyond. This book provides the first comprehensive introduction to the circle of ideas developed around the program, the prerequisites being only a basic knowledge of algebraic geometry. It will be of great interest to graduate students and researchers working in algebraic geometry and related fields.
Author: Bjorn Poonen
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 292
ISBN-13: 0817681701
DOWNLOAD EBOOK →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: 健爾·上野
Publisher: American Mathematical Soc.
Published: 1999
Total Pages: 178
ISBN-13: 0821808621
DOWNLOAD EBOOK →By studying algebraic varieties over a field, this book demonstrates how the notion of schemes is necessary in algebraic geometry. It gives a definition of schemes and describes some of their elementary properties.
