Algebraic geometry

Homogeneous spaces of linear algebraic groups lie at the crossroads of algebraic geometry, theory of algebraic groups, classical projective and enumerative geometry, harmonic analysis, and representation theory.

This book focuses on a large class of geometric objects in moduli theory and provides explicit computations to investigate their families.

to introduce these techniques and additional background is provided in appendices.

This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors.

This book presents four lectures on Rees rings and blow-ups, Koszul modules with applications to syzygies, Grobner bases and degenerations, and applications of Adams operations.

This book is an elementary introduction to some ideas and techniques that have revolutionized enumerative geometry: stable maps and quantum cohomology.

This textbook introduces exciting new developments and cutting-edge results on the theme of hyperbolicity.

This textbook provides an accessible introduction to the rich and beautiful area of hyperplane arrangement theory, where discrete mathematics, in the form of combinatorics and arithmetic, meets continuous mathematics, in the form of the topology and Hodge theory of complex algebraic varieties.

This work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory.

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

In recent years, new algorithms for dealing with rings of differential operators have been discovered and implemented.

One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems.

This book provides an introduction to categorical Donaldson-Thomas (DT) theory, a rapidly developing field which has close links to enumerative geometry, birational geometry, geometric representation theory and classical moduli problems in algebraic geometry.

The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their quotients.

Semi-Infinite Geometry is a theory of "e;doubly infinite-dimensional"e; geometric or topological objects.

The goal of this book is to provide an introduction to algebraic geometry accessible to students.

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

These notes are an expanded and updated version of a course of lectures which I gave at King's College London during the summer term 1979.

This monograph presents the basic concepts of hyperbolic Lobachevsky geometry and their possible applications to modern nonlinear applied problems in mathematics and physics, summarizing the findings of roughly the last hundred years.

The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface.

In this book we study Hilbert schemes of zero-dimensional subschemes of smooth varieties and several related parameter varieties of interest in enumerative geometry.

The articles in this volume study various cohomological aspects of algebraic varieties:- characteristic classes of singular varieties;- geometry of flag varieties;- cohomological computations for homogeneous spaces;- K-theory of algebraic varieties;- quantum cohomology and Gromov-Witten theory.

This volume consists of ten articles which provide an in-depth and reader-friendly survey of some of the foundational aspects of singularity theory.

Federico Gaeta (1923-2007) was a Spanish algebraic geometer who was a student of Severi.

Bifurcation of Maps and Applications

The theory presented in this work merges many concepts from mathematical optimization and real algebraic geometry.

This book contains a series of research papers on subjects related to the work of Niels Henrik Abel, written by some of the foremost specialists in their fields.

This EMS volume consists of two parts.

This advanced textbook provides a comprehensive and unified account of the moment problem.

Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago.

This book, the third book in the four-volume series in algebra, deals with important topics in homological algebra, including abstract theory of derived functors, sheaf co-homology, and an introduction to etale and l-adic co-homology.

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This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties.

This collection of surveys and research articles explores a fascinating class of varieties: Beauville surfaces.

The topological fundamental group of a smooth complex algebraic variety is poorly understood.

This book provides an introduction to geometric invariant theory from a differential geometric viewpoint.

This proceedings volume covers a range of research topics in algebra from the Southern Regional Algebra Conference (SRAC) that took place in March 2017.

Analytic Functions and Manifolds in Infinite Dimensional Spaces

This book explores toric topology, polyhedral products and related mathematics from a wide range of perspectives, collectively giving an overview of the potential of the areas while contributing original research to drive the subject forward in interesting new directions.

The Yau-Tian-Donaldson conjecture for anti-canonical polarization was recently solved affirmatively by Chen-Donaldson-Sun and Tian.