Higher Dimensional Algebraic Geometry PDF Download
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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 | : Thomas Peternell |
Publisher | : Birkhäuser |
Total Pages | : 221 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034888937 |
Download Geometry of Higher Dimensional Algebraic Varieties Book in PDF, ePub and Kindle
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 | : Bjorn Poonen |
Publisher | : Springer Science & Business Media |
Total Pages | : 292 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 0817681701 |
Download Arithmetic of Higher-Dimensional Algebraic Varieties Book in PDF, ePub and Kindle
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 | : Christopher D. Hacon |
Publisher | : Springer Science & Business Media |
Total Pages | : 206 |
Release | : 2011-02-02 |
Genre | : Mathematics |
ISBN | : 3034602901 |
Download Classification of Higher Dimensional Algebraic Varieties Book in PDF, ePub and Kindle
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 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 | : 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 | : J. Scott Carter |
Publisher | : World Scientific |
Total Pages | : 344 |
Release | : 1995 |
Genre | : Science |
ISBN | : 9789810220662 |
Download How Surfaces Intersect in Space Book in PDF, ePub and Kindle
This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.
Author | : D. Kaledin |
Publisher | : IOS Press |
Total Pages | : 356 |
Release | : 2008-06-05 |
Genre | : Mathematics |
ISBN | : 1607503255 |
Download Higher-Dimensional Geometry Over Finite Fields Book in PDF, ePub and Kindle
Number systems based on a finite collection of symbols, such as the 0s and 1s of computer circuitry, are ubiquitous in the modern age. Finite fields are the most important such number systems, playing a vital role in military and civilian communications through coding theory and cryptography. These disciplines have evolved over recent decades, and where once the focus was on algebraic curves over finite fields, recent developments have revealed the increasing importance of higher-dimensional algebraic varieties over finite fields. The papers included in this publication introduce the reader to recent developments in algebraic geometry over finite fields with particular attention to applications of geometric techniques to the study of rational points on varieties over finite fields of dimension of at least 2.
Author | : Andrew Ranicki |
Publisher | : Springer Science & Business Media |
Total Pages | : 669 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 3662120119 |
Download High-dimensional Knot Theory Book in PDF, ePub and Kindle
Bringing together many results previously scattered throughout the research literature into a single framework, this work concentrates on the application of the author's algebraic theory of surgery to provide a unified treatment of the invariants of codimension 2 embeddings, generalizing the Alexander polynomials and Seifert forms of classical knot theory.
Author | : Janos Kollár |
Publisher | : Cambridge University Press |
Total Pages | : 254 |
Release | : 2010-03-24 |
Genre | : Mathematics |
ISBN | : 9780511662560 |
Download Birational Geometry of Algebraic Varieties Book in PDF, ePub and Kindle
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.