Geometry Of Higher Dimensional Algebraic Varieties

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Geometry Of Higher Dimensional Algebraic Varieties

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Author : Thomas Peternell
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-03-20

Geometry Of Higher Dimensional Algebraic Varieties written by Thomas Peternell and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-03-20 with Mathematics categories.

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.

Higher Dimensional Varieties And Rational Points

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Author : K. Böröczky
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-07-10

Higher Dimensional Varieties And Rational Points written by K. Böröczky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-10 with Mathematics categories.

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.

Higher Dimensional Algebraic Geometry

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Author : Olivier Debarre
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-06-26

Higher Dimensional Algebraic Geometry written by Olivier Debarre and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-26 with Mathematics categories.

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.

Arithmetic Of Higher Dimensional Algebraic Varieties

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Author : Bjorn Poonen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Arithmetic Of Higher Dimensional Algebraic Varieties written by Bjorn Poonen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

One of the great successes of twentieth century mathematics has been the remarkable qualitative understanding of rational and integral points on curves, gleaned in part through the theorems of Mordell, Weil, Siegel, and Faltings. It has become clear that the study of rational and integral points has deep connections to other branches of mathematics: complex algebraic geometry, Galois and étale cohomology, transcendence theory and diophantine approximation, harmonic analysis, automorphic forms, and analytic number theory. This text, which focuses on higher dimensional varieties, provides precisely such an interdisciplinary view of the subject. It is a digest of research and survey papers by leading specialists; the book documents current knowledge in higher-dimensional arithmetic and gives indications for future research. It will be valuable not only to practitioners in the field, but to a wide audience of mathematicians and graduate students with an interest in arithmetic geometry.

Geometry Of Higher Dimensional Algebraic Varieties

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Author : Thomas Peternell
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

Geometry Of Higher Dimensional Algebraic Varieties written by Thomas Peternell and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

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.

Rational Curves On Algebraic Varieties

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Author : Janos Kollar
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-06-22

Rational Curves On Algebraic Varieties written by Janos Kollar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-22 with Mathematics categories.

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.

Classification Of Higher Dimensional Algebraic Varieties

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Author : Christopher D. Hacon
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-02-02

Classification Of Higher Dimensional Algebraic Varieties written by Christopher D. Hacon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-02-02 with Mathematics categories.

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.

The Geometry Of Some Special Arithmetic Quotients

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Author : Bruce Hunt
language : en
Publisher: Springer
Release Date : 2006-11-14

The Geometry Of Some Special Arithmetic Quotients written by Bruce Hunt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

The book discusses a series of higher-dimensional moduli spaces, of abelian varieties, cubic and K3 surfaces, which have embeddings in projective spaces as very special algebraic varieties. Many of these were known classically, but in the last chapter a new such variety, a quintic fourfold, is introduced and studied. The text will be of interest to all involved in the study of moduli spaces with symmetries, and contains in addition a wealth of material which has been only accessible in very old sources, including a detailed presentation of the solution of the equation of 27th degree for the lines on a cubic surface.

Higher Dimensional Birational Geometry

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Author : Kyoto Daigaku. Suri Kaiseki Kenkyujo
language : en
Publisher: Mathematical Soc of Japan
Release Date : 2002

Higher Dimensional Birational Geometry written by Kyoto Daigaku. Suri Kaiseki Kenkyujo and has been published by Mathematical Soc of Japan this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

This volume contains four papers written by participants of the international conference on Higher Dimensional Algebraic Varieties held at the Research Institute of Mathematical Sciences (RIMS) at Kyoto University (Japan). Rather than an ordinary proceedings of the conference, the editors have compiled a selection of independent, full expositions on topics of fundamental importance in algebraic geometry: moduli spaces of abelian surfaces, rational curves on algebraic varieties, 3-dimensional flips, and the theory of elliptic fibrations. The authors--including a Fields medalist and the founder of fundamental results in algebraic geometry--discuss the topics fully, giving complete proofs of new results, technical preparations, and an historical overview. The book is suitable for graduate students and research mathematicians interested in algebraic geometry.