Introduction to the Mori Program


Author: Kenji Matsuki
Publisher: Springer Science & Business Media
ISBN: 147575602X
Category: Mathematics
Page: 478
View: 5397

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Mori's Program is a fusion of the so-called Minimal Model Program and the IItaka Program toward the biregular and/or birational classification of higher dimensional algebraic varieties. The author presents this theory in an easy and understandable way with lots of background motivation. Prerequisites are those covered in Hartshorne's book "Algebraic Geometry." This is the first book in this extremely important and active field of research and will become a key resource for graduate students wanting to get into the area.

Algebraic and Geometric Combinatorics

Euroconference in Mathematics : Algebraic and Geometric Combinatorics, August 20-26, 2005, Anogia, Crete, Greece
Author: Christos A. Athanasiadis
Publisher: American Mathematical Soc.
ISBN: 0821840800
Category: Mathematics
Page: 324
View: 4398

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This volume contains original research and survey articles stemming from the Euroconference ""Algebraic and Geometric Combinatorics"". The papers discuss a wide range of problems that illustrate interactions of combinatorics with other branches of mathematics, such as commutative algebra, algebraic geometry, convex and discrete geometry, enumerative geometry, and topology of complexes and partially ordered sets. Among the topics covered are combinatorics of polytopes, lattice polytopes, triangulations and subdivisions, Cohen-Macaulay cell complexes, monomial ideals, geometry of toric surfaces, groupoids in combinatorics, Kazhdan-Lusztig combinatorics, and graph colorings. This book is aimed at researchers and graduate students interested in various aspects of modern combinatorial theories.

Snowbird Lectures in Algebraic Geometry

Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Algebraic Geometry : Presentations by Young Researchers, July 4-8, 2004
Author: Ravi Vakil
Publisher: American Mathematical Soc.
ISBN: 0821837192
Category: Mathematics
Page: 188
View: 1731

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A significant part of the 2004 Summer Research Conference on Algebraic Geometry (Snowbird, UT) was devoted to lectures introducing the participants, in particular, graduate students and recent Ph.D.'s, to a wide swathe of algebraic geometry and giving them a working familiarity with exciting, rapidly developing parts of the field. One of the main goals of the organizers was to allow the participants to broaden their horizons beyond the narrow area in which they are working. A fine selection of topics and a noteworthy list of contributors made the resulting collection of articles a useful resource for everyone interested in getting acquainted with the modern topic of algebraic geometry.The book consists of ten articles covering, among others, the following topics: the minimal model program, derived categories of sheaves on algebraic varieties, Kobayashi hyperbolicity, groupoids and quotients in algebraic geometry, rigid analytic varieties, and equivariant cohomology. Suitable for independent study, this unique volume is intended for graduate students and researchers interested in algebraic geometry.

Toric Varieties


Author: David A. Cox,John B. Little,Henry K. Schenck
Publisher: American Mathematical Soc.
ISBN: 0821848194
Category: Mathematics
Page: 841
View: 2216

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Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book covers the standard topics in toric geometry; a novel feature is that each of the first nine chapters contains an introductory section on the necessary background material in algebraic geometry. Other topics covered include quotient constructions, vanishing theorems, equivariant cohomology, GIT quotients, the secondary fan, and the minimal model program for toric varieties. The subject lends itself to rich examples reflected in the 134 illustrations included in the text. The book also explores connections with commutative algebra and polyhedral geometry, treating both polytopes and their unbounded cousins, polyhedra. There are appendices on the history of toric varieties and the computational tools available to investigate nontrivial examples in toric geometry. Readers of this book should be familiar with the material covered in basic graduate courses in algebra and topology, and to a somewhat lesser degree, complex analysis. In addition, the authors assume that the reader has had some previous experience with algebraic geometry at an advanced undergraduate level. The book will be a useful reference for graduate students and researchers who are interested in algebraic geometry, polyhedral geometry, and toric varieties.

Newsletter


Author: New Zealand Mathematical Society
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 9625

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Current Developments in Mathematics


Author: David Jerison,Barry Mazur,Wilfried Schmid,Tomasz Mrowka,Richard Stanley,Shing-Tung Yau
Publisher: N.A
ISBN: 9781571461346
Category: Mathematics
Page: 245
View: 2491

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Higher-Dimensional Algebraic Geometry


Author: Olivier Debarre
Publisher: Springer Science & Business Media
ISBN: 9780387952277
Category: Mathematics
Page: 234
View: 3228

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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.

Vorlesungen Über die Zahlentheorie der Quaternionen


Author: Adolf Hurwitz
Publisher: Springer-Verlag
ISBN: 3642475361
Category: Mathematics
Page: 76
View: 8213

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Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Books in Print


Author: N.A
Publisher: N.A
ISBN: N.A
Category: American literature
Page: N.A
View: 611

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Books in print is the major source of information on books currently published and in print in the United States. The database provides the record of forthcoming books, books in-print, and books out-of-print.

Mathematical works


Author: Helmut Wielandt
Publisher: Walter de Gruyter
ISBN: 9783110124538
Category: Mathematics
Page: 802
View: 2410

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Contains all the mathematical works of the 20th-century German mathematician except those on group theory, which comprise the first volume. Most are on matrix theory. Among them are 24 research papers arranged chronologically, many with commentary by specialists; lecture notes on the analytic theory of matrix groups; his series of contributions to the mathematical treatment of complex eigenvalue problems prepared during the Second World War; and 1973 lecture notes on selected topics of permutation groups. About half of the pieces are in German. No index. Annotation copyrighted by Book News, Inc., Portland, OR

Fünf Minuten Mathematik

100 Beiträge der Mathematik-Kolumne der Zeitung Die Welt
Author: Ehrhard Behrends
Publisher: Springer-Verlag
ISBN: 9783834800824
Category:
Page: 256
View: 5842

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Geometrische Methoden in der Invariantentheorie


Author: Hanspeter Kraft
Publisher: Springer-Verlag
ISBN: 3663101436
Category: Technology & Engineering
Page: 308
View: 7732

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In dieser Einführung geht es vor allem um die geometrischen Aspekte der Invariantentheorie. Die hauptsächliche Motivation bildet das Studium von Klassifikations- und Normalformenproblemen, die auch historisch der Ausgangspunkt für invariantentheoretische Untersuchungen waren.