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Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines
 
Hagen Meltzer Szczecin University, Szczecin, Poland
Front Cover for Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines
Available Formats:
Electronic ISBN: 978-1-4704-0409-3
Product Code: MEMO/171/808.E
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $40.80
Front Cover for Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines
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  • Front Cover for Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines
  • Back Cover for Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines
Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines
Hagen Meltzer Szczecin University, Szczecin, Poland
Available Formats:
Electronic ISBN:  978-1-4704-0409-3
Product Code:  MEMO/171/808.E
List Price: $68.00
MAA Member Price: $61.20
AMS Member Price: $40.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1712004; 139 pp
    MSC: Primary 14; 16;

    This work deals with weighted projective lines, a class of non-commutative curves modelled by Geigle and Lenzing on a graded commutative sheaf theory. They play an important role in representation theory of finite-dimensional algebras; the complexity of the classification of coherent sheaves largely depends on the genus of these curves. We study exceptional vector bundles on weighted projective lines and show in particular that the braid group acts transitively on the set of complete exceptional sequences of such bundles. We further investigate tilting sheaves on weighted projective lines and determine the Auslander-Reiten components of modules over their endomorphism rings. Finally we study tilting complexes in the derived category and present detailed classification results in the case of weighted projective lines of hyperelliptic type.

    Readership

    Graduate students and research mathematicians interested in algebraic geometry and representations of finite-dimensional algebras.

  • Table of Contents
     
     
    • Chapters
    • 1. Background
    • 2. Summary
    • 3. Weighted projective lines
    • 4. Mutations of exceptional sequences
    • 5. Tubular mutations
    • 6. Twisted mutations
    • 7. On the number of exceptional vector bundles
    • 8. Tilting sheaves
    • 9. Tilting complexes
    • 10. Hyperelliptic weighted projective lines
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Volume: 1712004; 139 pp
MSC: Primary 14; 16;

This work deals with weighted projective lines, a class of non-commutative curves modelled by Geigle and Lenzing on a graded commutative sheaf theory. They play an important role in representation theory of finite-dimensional algebras; the complexity of the classification of coherent sheaves largely depends on the genus of these curves. We study exceptional vector bundles on weighted projective lines and show in particular that the braid group acts transitively on the set of complete exceptional sequences of such bundles. We further investigate tilting sheaves on weighted projective lines and determine the Auslander-Reiten components of modules over their endomorphism rings. Finally we study tilting complexes in the derived category and present detailed classification results in the case of weighted projective lines of hyperelliptic type.

Readership

Graduate students and research mathematicians interested in algebraic geometry and representations of finite-dimensional algebras.

  • Chapters
  • 1. Background
  • 2. Summary
  • 3. Weighted projective lines
  • 4. Mutations of exceptional sequences
  • 5. Tubular mutations
  • 6. Twisted mutations
  • 7. On the number of exceptional vector bundles
  • 8. Tilting sheaves
  • 9. Tilting complexes
  • 10. Hyperelliptic weighted projective lines
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