<p>It has been estimated that, at the present stage of our knowledge, one could give a 200 semester course on commutative algebra and algebraic geometry without ever repeating himself. So any introduction to this subject must be highly selective. I first want to indicate what point of view guided the selection of material for this book. This introduction arose from lectures for students who had taken a basic course in algebra and could therefore be presumed to have a knowledge of linear algebra, ring and field theory, and Galois theory. The present text shouldn't require much more. In the lectures and in this text I have undertaken with the fewest possible auxiliary means to lead up to some recent results of commutative algebra and algebraic geometry concerning the representation of algebraic varieties as in tersections of the least possible number of hypersurfaces and- a closely related problem-with the most economical generation of ideals in Noetherian rings. The question of the equations needed to describe an algebraic variety was addressed by Kronecker in 1882. In the 1940s it was chiefly Perron who was interested in this question; his discussions with Severi made the problem known and contributed to sharpening the rei event concepts. Thanks to the general progress of commutative algebra many beautiful results in this circle of questions have been obtained, mainly after the solution of Serre's problem on projective modules. Because of their relatively elementary character they are especially suitable for an introduction to commutative algebra.</p>

Introduction to Commutative Algebra and Algebraic Geometry

Science & Math

Ernst Kunz

Mathematics

Birkhäuser Boston

This book, which grew out of lectures by E. Kunz for students with a background in algebra and algebraic geometry, develops local and global duality theory in the special case of (possibly singular) algebraic varieties over algebraically closed base fields. It describes duality and residue theorems in terms of Kahler differential forms and their residues. The properties of residues are introduced via local cohomology. Special emphasis is given to the relation between residues to classical results of algebraic geometry and their generalizations. The contribution by A. Dickenstein gives applications of residues and duality to polynomial solutions of constant coefficient partial differential equations and to problems in interpolation and ideal membership. D. A. Cox explains toric residues and relates them to the earlier text. The book is intended as an introduction to more advanced treatments and further applications of the subject, to which numerous bibliographical hints are given.

Residues and Duality for Projective Algebraic Varieties (University Lecture Series) (University Lecture Series, 47)

American Mathematical Society

See the best price to sell, buy, or rent books by Ernst Kunz. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Ernst Kunz

See the best price to sell, buy, or rent books by Ernst Kunz. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Introduction to Commutative Algebra and Algebraic Geometry

Residues and Duality for Projective Algebraic Varieties (University Lecture Series) (University Lecture Series, 47)