**University Lecture Series**

Volume: 47;
2008;
158 pp;
Softcover

MSC: Primary 14;
Secondary 32

Print ISBN: 978-0-8218-4760-2

Product Code: ULECT/47

List Price: $42.00

Individual Member Price: $33.60

**Electronic ISBN: 978-1-4704-1642-3
Product Code: ULECT/47.E**

List Price: $42.00

Individual Member Price: $33.60

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#### Supplemental Materials

# Residues and Duality for Projective Algebraic Varieties

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*Ernst Kunz; David A. Cox; Alicia Dickenstein*

with the assistance of and contributions by David A. Cox, Amherst College, MA, and Alicia Dickenstein, University of Buenos Aires, Argentina

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.

#### Readership

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

#### Table of Contents

# Table of Contents

## Residues and Duality for Projective Algebraic Varieties

- Cover Cover11 free
- Title page iii5 free
- Contents v7 free
- Preface vii9 free
- Glossary of notation ix11 free
- Local cohomology functors 117 free
- Local cohomology of noetherian affine schemes 622
- Čech cohomology 1127
- Koszul complexes and local cohomology 2238
- Residues and local cohomology for power series rings 3551
- The cohomology of projective schemes 4763
- Duality and residue theorems for projective space 5268
- Traces, complementary modules, and differents 6581
- The sheaf of regular differential forms on an algebraic variety 8197
- Residues for algebraic varieties. Local duality 89105
- Duality and residue theorems for projective varieties 100116
- Complete duality 110126
- Applications of residues and duality 115131
- Toric residues 128144
- Bibliography 151167
- Index 155171 free
- Back Cover Back Cover1177