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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
Front Cover for Residues and Duality for Projective Algebraic Varieties
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
Front Cover for Residues and Duality for Projective Algebraic Varieties
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  • Front Cover for Residues and Duality for Projective Algebraic Varieties
  • Back Cover for Residues and Duality for Projective Algebraic Varieties
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.

    Readership

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

  • Table of Contents
     
     
    • 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
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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.

Readership

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
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