Algebraic geometry

In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry.

Lecture notes and research articles on the use of torsors and étale homotopy in algebraic and arithmetic geometry.

It is a pleasure to welcome you to the proceedings of the second International Castle Meeting on Coding Theory and its Applications, held at La Mota Castle in Medina del Campo.

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind.

This book takes an in-depth look at abelian relations of codimension one webs in the complex analytic setting.

This monograph introduces readers to locally conformally Kahler (LCK) geometry and provides an extensive overview of the most current results.

The NATO Advanced Study Institute on "e;The Arithmetic and Geometry of Algebraic Cycles"e; was held at the Banff Centre for Conferences in Banff (Al- berta, Canada) from June 7 until June 19, 1998.

Based on the Simons Symposia held in 2015, the proceedings in this volume focus on rational curves on higher-dimensional algebraic varieties and applications of the theory of curves to arithmetic problems.

The goal of the book is to present, in a complete and comprehensive way, areas of current research interlacing around the Poncelet porism: dynamics of integrable billiards, algebraic geometry of hyperelliptic Jacobians, and classical projective geometry of pencils of quadrics.

Customarily, the framework of algebraic geometry has been worked over an algebraically closed field of characteristic zero, say, over the complex number field.

This book is based on courses given at Columbia University on vector bun- dles (1988) and on the theory of algebraic surfaces (1992), as well as lectures in the Park City lIAS Mathematics Institute on 4-manifolds and Donald- son invariants.

This original monograph investigates several unsolved problems that currently exist in coding theory.

This is the second of approximately four volumes that the authors plan to write in their examination of all the claims made by S.

An Introduction to the Mathematical Theory of Geophysical Fluid Dynamics

Preface Among the various branches of mathematics, number theory is characterized to a lesser degree by its primary subject ("e;integers"e;) than by a psychologi- cal attitude.

Resolution of singularities is notorious as a difficult topic within algebraic geometry.

Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.

In this volume, the authors construct a theory of weights on the log crystalline cohomologies of families of open smooth varieties in characteristic p>0, by defining and constructing four filtered complexes.

An up-to-date survey of research in singularity theory.

This book provides an introduction to state-of-the-art applications of homotopy theory to arithmetic geometry.

This book is based on the lectures given at the Oberwolfach Seminar held in Fall 2021.

This undergraduate and postgraduate text will familiarise readers with interval arithmetic and related tools to gain reliable and validated results and logically correct decisions for a variety of geometric computations plus the means for alleviating the effects of the errors.

This book is based on the lectures given at the Oberwolfach Seminar on Tropical Algebraic Geometry in October 2004.

For the past several decades the theory of automorphic forms has become a major focal point of development in number theory and algebraic geometry, with applications in many diverse areas, including combinatorics and mathematical physics.

This volume contains the expanded versions of the lectures given by the authors at the C.

Schubert varieties and degeneracy loci have a long history in mathematics, starting from questions about loci of matrices with given ranks.

This monograph deals with the Hadamard products of algebraic varieties.

This study of graded rings includes the first systematic account of graded Grothendieck groups.

For the most part, this book is the translation from Japanese of the earlier book written jointly by Koji Doi and the author who revised it substantially for the English edition.

From the reviews: "e;This book gives a thorough introduction to several theories that are fundamental to research on modular forms.

This volume of expository papers is the outgrowth of a conference in combinatorics and invariant theory.

In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities.

In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130].

This monograph presents the current status of a rapidly developing part of several complex variables, motivated by the applicability of effective results to algebraic geometry and differential geometry.

This book studies the interplay between the geometry and topology of locally symmetric spaces, and the arithmetic aspects of the special values of L-functions.

The first 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.

Capacity is a measure of size for sets, with diverse applications in potential theory, probability and number theory.

This book discusses the importance of flag varieties in geometric objects and elucidates its richness as interplay of geometry, combinatorics and representation theory.

This book presents progress on two open problems within the framework of algebraic geometry and commutative algebra: Grobner's problem regarding the arithmetic Cohen-Macaulayness (aCM) of projections of Veronese varieties, and the problem of determining the structure of the algebra of invariants of finite groups.

In the last five years there has been very significant progress in the development of transcendence theory.

Topics in Arithmetical Functions

The present book is devoted to a study of relative Prufer rings and Manis valuations, with an eye to application in real and p-adic geometry.