Algebraic geometry

How I have (re-)written this book The book the reader has in hand was supposed to be a new edition of [14].

In recent years, extensive research has been conducted by eminent mathematicians and engineers whose results and proposed problems are presented in this new volume.

This book is the outcome of research initiatives formed during the special ``Research Trimester on Multiple Zeta Values, Multiple Polylogarithms, and Quantum Field Theory' at the ICMAT (Instituto de Ciencias Matematicas, Madrid) in 2014.

The invariant theory of non-reductive groups has its roots in the 19th century but has seen some very interesting developments in the past twenty years.

A classic treatment of the geometry of orthogonal spaces from the acclaimed Annals of Mathematics Studies seriesPrinceton University Press is proud to have published the Annals of Mathematics Studies since 1940.

The collection of papers in this volume represents recent advances in the under- standing of the geometry and topology of singularities.

If you have not heard about cohomology, this book may be suited for you.

In the Teichmuller theory of Riemann surfaces, besides the classical theory of quasi-conformal mappings, vari- ous approaches from differential geometry and algebraic geometry have merged in recent years.

This book explores determinantal ideals of square matrices from the perspective of commutative algebra, with a particular emphasis on linear matrices.

It was the aim of the Erlangen meeting in May 1988 to bring together number theoretists and algebraic geometers to discuss problems of common interest, such as moduli problems, complex tori, integral points, rationality questions, automorphic forms.

The theory of hyperbolic groups has its starting point in a fundamental paper by M.

This book provides a systematic treatment of algebraic and topological properties of convex sets (possibly non-closed or unbounded) in the n-dimensional Euclidean space.

Cohomology of Completions

This book arose from a conference on "e;Singularities and Computer Algebra"e; which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel's 70th birthday.

 This volume is the proceedings of the Conference on Algebra and Algebraic Geometry with Applications which was held July 19 - 26, 2000, at Purdue University to honor Professor Shreeram S.

I am pleased to participate in this Summer School and look forward to sharing some ideas with you over the next few days.

This book is devoted to the structure of the absolute Galois groups of certain algebraic extensions of the field of rational numbers.

Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research.

This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Grobner bases) and geometry (via quiver theory).

This unique collection of new and classical problems provides full coverage of algebraic inequalities.

This book provides a systematic account of several breakthroughs in the modern theory of zeta functions.

This volume consists of a collection of articles for the proceedings of the 40th Taniguchi Symposium Analysis and Geometry in Several Complex Variables held in Katata, Japan, on June 23-28, 1997.

This volume presents a panorama of the diverse activities organized by V.

We investigate GIT quotients of polarized curves.

Matched Asymptotic Expansions and Singular Perturbations

Spherical buildings are certain combinatorial simplicial complexes intro- duced, at first in the language of "e;incidence geometries,"e; to provide a sys- tematic geometric interpretation of the exceptional complex Lie groups.

This second edition has been completely restructured, resulting in a compelling description of vector analysis from its first appearance as a byproduct of Hamilton's quaternions to the use of vectors in solving geometric problems.

The second of a two-part volume, this collection offers a unifying vision of algebraic geometry, exploring its evolution over the last four decades as well as state-of-the art research.

Riemannian, symplectic and complex geometry are often studied by means ofsolutions to systems ofnonlinear differential equations, such as the equa- tions of geodesics, minimal surfaces, pseudoholomorphic curves and Yang- Mills connections.

This volume presents the theory of partial differential equations (PDEs) from a modern geometric point of view so that PDEs can be characterized by using either technique of differential geometry or algebraic geometry.

This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems.

The book is a reproduction of a course of lectures delivered by the author in 1983-84 which appeared in the Brandeis Lecture Notes series.

This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes.

This book is an extended and revised version of "e;Numerical Semigroups with Applications,"e; published by Springer as part of the RSME series.

Providing a timely description of the present state of the art of moduli spaces of curves and their geometry, this volume is written in a way which will make it extremely useful both for young people who want to approach this important field, and also for established researchers, who will find references, problems, original expositions, new viewpoints, etc.

Holomorphic Functions, Domains of Holomorphy and Local Properties

Surveys and articles on recent developments in pure and applied singularity theory.

Integral transforms, such as the Laplace and Fourier transforms, have been major tools in mathematics for at least two centuries.

A systematic exposition of the basics of period domains.

This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi-Yau varieties and string theory.