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Residues and Duality for Projective Algebraic Varieties

Ernst Kunz University of Regensburg, Regensburg, Germany
David A. Cox Amherst College, Amherst, MA
Alicia Dickenstein University of Buenos Aires, Buenos Aires, Argentina
with the assistance of and contributions by David A. Cox, Amherst College, MA, and Alicia Dickenstein, University of Buenos Aires, Argentina
Available Formats:
Softcover ISBN: 978-0-8218-4760-2
Product Code: ULECT/47
List Price: $45.00 MAA Member Price:$40.50
AMS Member Price: $36.00 Electronic ISBN: 978-1-4704-1642-3 Product Code: ULECT/47.E List Price:$42.00
MAA Member Price: $37.80 AMS Member Price:$33.60
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List Price: $67.50 MAA Member Price:$60.75
AMS Member Price: $54.00 Click above image for expanded view Residues and Duality for Projective Algebraic Varieties Ernst Kunz University of Regensburg, Regensburg, Germany David A. Cox Amherst College, Amherst, MA Alicia Dickenstein University of Buenos Aires, Buenos Aires, Argentina with the assistance of and contributions by David A. Cox, Amherst College, MA, and Alicia Dickenstein, University of Buenos Aires, Argentina Available Formats:  Softcover ISBN: 978-0-8218-4760-2 Product Code: ULECT/47  List Price:$45.00 MAA Member Price: $40.50 AMS Member Price:$36.00
 Electronic ISBN: 978-1-4704-1642-3 Product Code: ULECT/47.E
 List Price: $42.00 MAA Member Price:$37.80 AMS Member Price: $33.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$67.50 MAA Member Price: $60.75 AMS Member Price:$54.00
• Book Details

University Lecture Series
Volume: 472008; 158 pp
MSC: Primary 14; Secondary 32;

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.

• Articles
• Chapter 1. Local cohomology functors
• Chapter 2. Local cohomology of noetherian affine schemes
• Chapter 3. Čech cohomology
• Chapter 4. Koszul complexes and local cohomology
• Chapter 5. Residues and local cohomology for power series rings
• Chapter 6. The cohomology of projective schemes
• Chapter 7. Duality and residue theorems for projective space
• Chapter 8. Traces, complementary modules, and differents
• Chapter 9. The sheaf of regular differential forms on an algebraic variety
• Chapter 10. Residues for algebraic varieties. Local duality
• Chapter 11. Duality and residue theorems for projective varieties
• Chapter 12. Complete duality
• Alicia Dickenstein - Chapter 13. Applications of residues and duality
• David A. Cox - Chapter 14. Toric residues

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 472008; 158 pp
MSC: Primary 14; Secondary 32;

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.

• Articles
• Chapter 1. Local cohomology functors
• Chapter 2. Local cohomology of noetherian affine schemes
• Chapter 3. Čech cohomology
• Chapter 4. Koszul complexes and local cohomology
• Chapter 5. Residues and local cohomology for power series rings
• Chapter 6. The cohomology of projective schemes
• Chapter 7. Duality and residue theorems for projective space
• Chapter 8. Traces, complementary modules, and differents
• Chapter 9. The sheaf of regular differential forms on an algebraic variety
• Chapter 10. Residues for algebraic varieties. Local duality
• Chapter 11. Duality and residue theorems for projective varieties
• Chapter 12. Complete duality
• Alicia Dickenstein - Chapter 13. Applications of residues and duality
• David A. Cox - Chapter 14. Toric residues
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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