Algebraic geometry

This book discusses general topological algebras; space C(T,F) of continuous functions mapping T into F as an algebra only (with pointwise operations); and C(T,F) endowed with compact-open topology as a topological algebra C(T,F,c).

This book is about three seemingly independent areas of mathematics: combinatorial group theory, the theory of Lie algebras and affine algebraic geometry.

The 2007 Abel Symposium took place at the University of Oslo in August 2007.

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

This comprehensive introduction to algebraic complexity theory presents new techniques for analyzing P vs NP and matrix multiplication.

Ruled varieties are unions of a family of linear spaces.

Providing an introduction to both classical and modern techniques in projective algebraic geometry, this monograph treats the geometrical properties of varieties embedded in projective spaces, their secant and tangent lines, the behavior of tangent linear spaces, the algebro-geometric and topological obstructions to their embedding into smaller projective spaces, and the classification of extremal cases.

The study of geometry can play an important role in stimulating mathematical imagination and intuition, particularly in its relation to algebra.

[From the foreword by B.

This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics- such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics- and in theoretical physics such as quantum field theory and string theory.

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.

Dieses Buch gibt eine Einführung in die Algebraische Geometrie.

Nigel Hitchin is one of the world's foremost figures in the fields of differential and algebraic geometry and their relations with mathematical physics, and he has been Savilian Professor of Geometry at Oxford since 1997.

Systems of polynomial equations arise throughout mathematics, science, and engineering.

A workshop on Singularities, Bifurcation and Dynamics was held at Warwick in July 1989 as part of a year-long symposium on Singularity Theory and its applications.

This volume presents a collection of results related to the BSD conjecture, based on the first two India-China conferences on this topic.

Recent developments in various algebraic structures and the applications of those in different areas play an important role in Science and Technology.

This book examines the life and work of mathematician Giovanni Battista Guccia, founder of the Circolo Matematico di Palermo and its renowned journal, the Rendiconti del Circolo matematico di Palermo.

Higher-Dimensional Algebraic Geometry studies the classification theory of algebraic varieties.

This comprehensive reference begins with a review of the basics followed by a presentation of flag varieties and finite- and infinite-dimensional representations in classical types and subvarieties of flag varieties and their singularities.

Considering integral transformations of Volterra type, F.

This textbook provides an essential introduction to Lie groups, presenting the theory from its fundamental principles.

This is the fourth volume of the Handbook of Geometry and Topology of Singularities, a series that aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research.

This two volume work on "e;Positivity in Algebraic Geometry"e; contains a contemporary account of a body of work in complex algebraic geometry loosely centered around the theme of positivity.

This textbook on combinatorial commutative algebra focuses on properties of monomial ideals in polynomial rings and their connections with other areas of mathematics such as combinatorics, electrical engineering, topology, geometry, and homological algebra.

Based on lectures held at the 8th edition of the series of summer schools in Villa de Leyva since 1999, this book presents an introduction to topics of current interest at the interface of geometry, algebra, analysis, topology and theoretical physics.

This volume collects contributions from speakers at the INdAM Workshop "e;Birational Geometry and Moduli Spaces"e;, which was held in Rome on 11-15 June 2018.

This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces.

Elementary particles in this book exist as Solitons in-and-of the fabric of spacetime itself.

This book provides an elementary introduction, complete with detailed proofs, to the celebrated tilings of the plane discovered by Sir Roger Penrose in the '70s.

From the reviews:"e;The book.

Algebraic K-Theory has become an increasingly active area of research.

The algebraic techniques developed by Kakde will almost certainly lead eventually to major progress in the study of congruences between automorphic forms and the main conjectures of non-commutative Iwasawa theory for many motives.

This highly regarded book is back in print and now updated to reflect recent advances in the field.

Abelian varieties are a natural generalization of elliptic curves to higher dimensions, whose geometry and classification are as rich in elegant results as in the one-dimensional ease.

Hilbert Functions play major roles in Algebraic Geometry and Commutative Algebra, and are becoming increasingly important also in Computational Algebra.

This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "e;Automorphic Forms and L-Functions"e;, held at the University of Heidelberg in 2016.

This monograph establishes a general context for the cohomological use of Hironaka's theorem on the resolution of singularities.

The lectures contained in this book were presented at Harvard University in June 1979.

Can artificial intelligence learn mathematics?

The notes in this volume correspond to advanced courses held at the Centre de Recerca Matematica as part of the research program in Arithmetic Geometry in the 2009-2010 academic year.