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Residues and Duality for Projective Algebraic Varieties
Ernst Kunz, University of Regensburg, Germany
with the assistance of and contributions by David A. Cox, Amherst College, MA, and Alicia Dickenstein, University of Buenos Aires, Argentina
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University Lecture Series
2008; 158 pp; softcover
Volume: 47
ISBN-10: 0-8218-4760-0
ISBN-13: 978-0-8218-4760-2
List Price: US$40 Member Price: US$32
Order Code: ULECT/47

Homotopy Theory of Schemes - Fabien Morel

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 Kähler 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.

Graduate students and research mathematicians interested in algebra, algebraic geometry, complex analyis, and computer algebra.