Higher-Dimensional Algebraic Geometry


Author: Olivier Debarre
Publisher: Springer Science & Business Media
ISBN: 147575406X
Category: Mathematics
Page: 234
View: 4593

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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


Author: Christopher D. Hacon,Sándor Kovács
Publisher: Springer Science & Business Media
ISBN: 3034602901
Category: Mathematics
Page: 220
View: 1694

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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.

Proceedings of the International Congress of Mathematicians

Madrid, August 22-30, 2006
Author: Marta Sanz Solé
Publisher: Amer Mathematical Society
ISBN: 9783037190227
Category: Mathematics
Page: 4500
View: 1461

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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


Author: New Zealand Mathematical Society
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 986

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Aspects of Brownian Motion


Author: Roger Mansuy,Marc Yor
Publisher: Springer Science & Business Media
ISBN: 9783540499664
Category: Mathematics
Page: 200
View: 507

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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.

Positivity in algebraic geometry 2


Author: R.K. Lazarsfeld,University of Michigan Staff
Publisher: Springer Science & Business Media
ISBN: 9783540225348
Category: Mathematics
Page: 385
View: 6231

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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".

Algebraische Zahlentheorie


Author: Jürgen Neukirch
Publisher: Springer-Verlag
ISBN: 3540376631
Category: Mathematics
Page: 595
View: 6024

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Algebraische Zahlentheorie: eine der traditionsreichsten und aktuellsten Grunddisziplinen der Mathematik. Das vorliegende Buch schildert ausführlich Grundlagen und Höhepunkte. Konkret, modern und in vielen Teilen neu. Neu: Theorie der Ordnungen. Plus: die geometrische Neubegründung der Theorie der algebraischen Zahlkörper durch die "Riemann-Roch-Theorie" vom "Arakelovschen Standpunkt", die bis hin zum "Grothendieck-Riemann-Roch-Theorem" führt.

Applied Stochastic Control of Jump Diffusions


Author: Bernt Øksendal,Agnès Sulem
Publisher: Springer
ISBN: 9783540698258
Category: Business & Economics
Page: 262
View: 6811

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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
Author: Peter K. Friz,Martin Hairer
Publisher: N.A
ISBN: 9783319083339
Category:
Page: 268
View: 6871

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