From the reviews:
"This book surveys an elegant new subject which has developed out of the cohomological treatment of class field theory by E. Artin and J. Tate. The bulk of the early contributions were by Tate, and we are greatly indebted to the author for publishing them in his very lucid style. Many others have made impressive discoveries in the field science. [...] An Appendix by J.-L. Verier covers duality in profinite groups."M. ...

This new edition describes the geometric part of the author's 1965 proof of desingularization of algebraic surfaces and solids in nonzero characteristic. The book also provides a self-contained introduction to birational algebraic geometry, based only on basic commutative algebra. In addition, it gives a short proof of analytic desingularization in characteristic zero for any dimension found in 1996 and based on a new avatar of an algorithmic ...

Contents: J.-P. Demailly: L(2) Vanishing Theorems for Positive Line Bundles and Adjunction Theory.- T. Peternell: Manifolds of Semi-Positive Curvature.- G. Tian: Kähler-Einstein Metrics on Algebraic Manifolds.- A. Tyurin: Six Lectures on Four Manifolds ...

This book covers the theory of algebraic surfaces and holomorphic vector bundles in an integrated manner. It is aimed at graduate students who have had a thorough first year course in algebraic geometry (at the level of Hartshorne's ALGEBRAIC GEOMETRY), as well as more advanced graduate students and researchers in the areas of algebraic geometry, gauge thoery, or 4-manifold topolgogy. Many of the results on vector bundles should also be of ...

Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks. These notes, from a summer school in Thurnau, aim to give an introduction to these topics, and to describe recent progress on these problems. There are interesting interactions with the algebra of symmetric functions and combinatorics, as well as the geometry of flag manifolds and intersection theory and ...

This book treats the theory of representations of homogeneous polynomials as sums of powers of linear forms. The first two chapters are introductory, and focus on binary forms and Waring's problem. Then the author's recent work is presented mainly on the representation of forms in three or more variables as sums of powers of relatively few linear forms. The methods used are drawn from seemingly unrelated areas of commutative algebra and ...

This book constitutes the refereed post-conference proceedings of the Second International Algorithmic Number Theory Symposium, ANTS-II, held in Talence, France in May 1996.The 35 revised full papers included in the book were selected from a variety of submissions. They cover a broad spectrum of topics and report state-of-the-art research results in computational number theory and complexity theory. Among the issues addressed are number fields ...

This volume presents the proceedings of the first
French-Soviet workshop on algebraic coding, held in Paris in
July 1991. The idea for the workshop, born in Leningrad (now
St. Petersburg) in 1990, was to bring together some of the
best Soviet coding theorists. Scientists from France,
Finland, Germany, Israel, Italy, Spain, and the United
States also attended.
The papers in the volume fall rather naturally into ...

The main themes of this book are to establish the triple formula without any hypotheses on the genericity of the morphism, and to develop a theory of complete quadruple points, which is a first step towards proving the quadruple point formula under less restrictive hypotheses.This book should be of interest to graduate students and researchers in the field of algebraic geometry. The reader is expected to have some basic knowledge of enumerative ...

This is the second volume of the new subseries "Invariant Theory and Algebraic Transformation Groups". The aim of the survey by A. Bialynicki-Birula is to present the main trends and achievements of research in the theory of quotients by actions of algebraic groups. This theory contains geometric invariant theory with various applications to problems of moduli theory. The contribution by J. Carrell treats the subject of torus actions on ...