Introduction to Intersection Theory in Algebraic Geometry

Author: William Fulton

Publisher: American Mathematical Soc.

ISBN: 0821807048

Category: Mathematics

Page: 82

View: 4297

This book introduces some of the main ideas of modern intersection theory, traces their origins in classical geometry and sketches a few typical applications. It requires little technical background: much of the material is accessible to graduate students in mathematics. A broad survey, the book touches on many topics, most importantly introducing a powerful new approach developed by the author and R. MacPherson. It was written from the expository lectures delivered at the NSF-supported CBMS conference at George Mason University, held June 27-July 1, 1983.The author describes the construction and computation of intersection products by means of the geometry of normal cones. In the case of properly intersecting varieties, this yields Samuel's intersection multiplicity; at the other extreme it gives the self-intersection formula in terms of a Chern class of the normal bundle; in general it produces the excess intersection formula of the author and R. MacPherson. Among the applications presented are formulas for degeneracy loci, residual intersections, and multiple point loci; dynamic interpretations of intersection products; Schubert calculus and solutions to enumerative geometry problems; and Riemann-Roch theorems.

An Invitation to Algebraic Geometry

Author: Karen E. Smith,Lauri Kahanpää,Pekka Kekäläinen,William Traves

Publisher: Springer Science & Business Media

ISBN: 1475744978

Category: Mathematics

Page: 164

View: 354

This is a description of the underlying principles of algebraic geometry, some of its important developments in the twentieth century, and some of the problems that occupy its practitioners today. It is intended for the working or the aspiring mathematician who is unfamiliar with algebraic geometry but wishes to gain an appreciation of its foundations and its goals with a minimum of prerequisites. Few algebraic prerequisites are presumed beyond a basic course in linear algebra.

Polytopes, Rings, and K-Theory

Author: Winfried Bruns,Joseph Gubeladze

Publisher: Springer Science & Business Media

ISBN: 0387763562

Category: Mathematics

Page: 461

View: 2945

This book examines interactions of polyhedral discrete geometry and algebra. What makes this book unique is the presentation of several central results in all three areas of the exposition - from discrete geometry, to commutative algebra, and K-theory.

Algebraic Geometry

A Concise Dictionary

Author: Elena Rubei

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110316234

Category: Mathematics

Page: 239

View: 1901

Algebraic geometry is one of the most classic subjects of university research in mathematics. It has a very complicated language that makes life very difficult for beginners. This book is a little dictionary of algebraic geometry: for every of the most common words in algebraic geometry, it contains its definition, several references and the statements of the main theorems about that term (without their proofs). Also some terms of other subjects, close to algebraic geometry, have been included. It was born to help beginners that know some basic facts of algebraic geometry, but not every basic fact, to follow seminars and to read papers, by providing them with basic definitions and statements. The form of a dictionary makes it very easy and quick to consult.

Singular Loci of Schubert Varieties

Author: Sara Billey,Venkatramani Lakshmibai

Publisher: Birkhauser


Category: Mathematics

Page: 251

View: 9895

The study of singular loci, an important sub-discipline of Schubert varieties, lies at the crossroads of representation theory, algebraic geometry, and combinatorics. To present a clearer understanding of the subject, the authors have recreated and restructured the various theories and approaches previously available only in journal articles. The book gives a systematic presentation of a wide range of topics and presents new results with sufficient examples, as well as numerous tables -- none of which are found elsewhere in the mathematics literature.

Topics in Algebra

Author: Jan Krempa,Stanisław Balcerzyk,Daniel Simson,Wolfgang Vogel,International Conference on Representations of Algebras

Publisher: N.A

ISBN: 9788301095796

Category: Rings (Algebra)

Page: N.A

View: 2303

Computer Algebra in Scientific Computing

8th International Workshop, CASC 2005, Kalamata, Greece, September 12-16, 2005, Proceedings

Author: Victor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhtsov

Publisher: Springer


Category: Computers

Page: 502

View: 301

This book constitutes the refereed proceedings of the 8th International Workshop on Computer Algebra in Scientific Computing, CASC 2005, held in Kalamata, Greece in September 2005. The 41 revised full papers presented were carefully reviewed and selected from 75 submissions. The topics addressed in the workshop cover all the basic areas of scientific computing as they benefit from the application of computer algebra methods and software: algebraic methods for nonlinear polynomial equations and inequalities, symbolic-numeric methods for differential and differential-algebraic equations, algorithmic and complexity considerations in computer algebra, algebraic methods in geometric modelling, aspects of computer algebra programming languages, automatic reasoning in algebra and geometry, complexity of algebraic problems, exact and approximate computation, parallel symbolic-numeric computation, Internet accessible symbolic and numeric computation, problem-solving environments, symbolic and numerical computation in systems engineering and modelling, computer algebra in industry, solving problems in the natural sciences, numerical simulation using computer algebra systems, mathematical communication.

Punctured Torus Groups and 2-Bridge Knot Groups (I)

Author: Hirotaka Akiyoshi,Makoto Sakuma,Masaaki Wada,Yasushi Yamashita

Publisher: Springer


Category: Mathematics

Page: 256

View: 6608

Here is the first part of a work that provides a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. It offers an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.

Solitons in Two-Dimensional Shallow Water

Author: Yuji Kodama

Publisher: SIAM

ISBN: 1611975522

Category: Science

Page: 252

View: 687

Web-like waves, often observed on the surface of shallow water, are examples of nonlinear waves. They are generated by nonlinear interactions among several obliquely propagating solitary waves, also known as solitons. In this book, modern mathematical tools—algebraic geometry, algebraic combinatorics, and representation theory, among others—are used to analyze these two-dimensional wave patterns. The author’s primary goal is to explain some details of the classification problem of the soliton solutions of the KP equation (or KP solitons) and their applications to shallow water waves. This book is intended for researchers and graduate students.