Higher-Dimensional Algebraic Geometry

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Author: Olivier Debarre

Publisher: Springer Science & Business Media

ISBN: 147575406X

Category: Mathematics

Page: 234

View: 5959

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.

Classification of Higher Dimensional Algebraic Varieties

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Author: Christopher D. Hacon,Sándor Kovács

Publisher: Springer Science & Business Media

ISBN: 3034602901

Category: Mathematics

Page: 220

View: 6779

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.

Geometry of Higher Dimensional Algebraic Varieties

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Author: Thomas Peternell,Joichi Miyaoka

Publisher: Springer Science & Business Media

ISBN: 9783764354909

Category: Mathematics

Page: 218

View: 5001

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.

Proceedings of the International Congress of Mathematicians

Madrid, August 22-30, 2006

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Author: Marta Sanz Solé

Publisher: Amer Mathematical Society

ISBN: 9783037190227

Category: Mathematics

Page: 4500

View: 937

The International Congress of Mathematicians (ICM) is held every four years. It is a major scientific event, bringing together mathematicians from all over the world and demonstrating the vital role that mathematics play in our society. In particular, the Fields Medals are awarded to recognize outstanding mathematical achievement. At the same time, the International Mathematical Union awards the Nevanlinna Prize for work in the field of theoretical computer science. The proceedings of ICM 2006, published as a three-volume set, present an overview of current research in all areas of mathematics and provide a permanent record the congress. The first volume features the works of Fields Medallists and the Nevanlinna Prize winner, the plenary lectures, and the speeches and pictures of the opening and closing ceremonies and award sessions. The other two volumes present the invited lectures, arranged according to their mathematical subject. Information for our distributors: Distributed within the Americas by the American Mathematical Society. All commerical channel discounts apply.

Newsletter

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Author: New Zealand Mathematical Society

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 5107

Positivity in algebraic geometry 2

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Author: R.K. Lazarsfeld,University of Michigan Staff

Publisher: Springer Science & Business Media

ISBN: 9783540225348

Category: Mathematics

Page: 385

View: 1983

This two volume work on "Positivity in Algebraic Geometry" contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity. Topics in Volume I include ample line bundles and linear series on a projective variety, the classical theorems of Lefschetz and Bertini and their modern outgrowths, vanishing theorems, and local positivity. Volume II begins with a survey of positivity for vector bundles, and moves on to a systematic development of the theory of multiplier ideals and their applications. A good deal of this material has not previously appeared in book form, and substantial parts are worked out here in detail for the first time. At least a third of the book is devoted to concrete examples, applications, and pointers to further developments. Whereas Volume I is more elementary, the present Volume II is more at the research level and somewhat more specialized. Both volumes are also available as hardcover edition as Vols. 48 and 49 in the series "Ergebnisse der Mathematik und ihrer Grenzgebiete".

Aspects of Brownian Motion

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Author: Roger Mansuy,Marc Yor

Publisher: Springer Science & Business Media

ISBN: 9783540499664

Category: Mathematics

Page: 200

View: 7330

Stochastic calculus and excursion theory are very efficient tools for obtaining either exact or asymptotic results about Brownian motion and related processes. This book focuses on special classes of Brownian functionals, including Gaussian subspaces of the Gaussian space of Brownian motion; Brownian quadratic funtionals; Brownian local times; Exponential functionals of Brownian motion with drift; Time spent by Brownian motion below a multiple of its one-sided supremum.

Applied Stochastic Control of Jump Diffusions

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Author: Bernt Øksendal,Agnès Sulem

Publisher: Springer

ISBN: 9783540698258

Category: Business & Economics

Page: 262

View: 439

Here is a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications. Discussion includes the dynamic programming method and the maximum principle method, and their relationship. The text emphasises real-world applications, primarily in finance. Results are illustrated by examples, with end-of-chapter exercises including complete solutions. The 2nd edition adds a chapter on optimal control of stochastic partial differential equations driven by Lévy processes, and a new section on optimal stopping with delayed information. Basic knowledge of stochastic analysis, measure theory and partial differential equations is assumed.

A Course on Rough Paths

With an Introduction to Regularity Structures

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Author: Peter K. Friz,Martin Hairer

Publisher: N.A

ISBN: 9783319083339

Category:

Page: 268

View: 4757

Elementare Algebraische Geometrie

Grundlegende Begriffe und Techniken mit zahlreichen Beispielen und Anwendungen

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Author: Klaus Hulek

Publisher: Springer-Verlag

ISBN: 3322802213

Category: Mathematics

Page: 167

View: 323

Dieses Buch gibt eine Einführung in die Algebraische Geometrie. Ziel ist es, die grundlegenden Begriffe und Techniken der algebraischen Geometrie zusammen mit einer Reihe von Beispielen darzustellen.