Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines
Share this pageHagen Meltzer
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.
Table of Contents
Table of Contents
Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines
- Contents v6 free
- Abstract vii8 free
- Chapter 1. Background 110 free
- Chapter 2. Summary 918
- Chapter 3. Weighted projective lines 1726
- Chapter 4. Mutations of exceptional sequences 2736
- Chapter 5. Tubular mutations 3746
- Chapter 6. Twisted mutations 4756
- Chapter 7. On the number of exceptional vector bundles 5564
- Chapter 8. Tilting sheaves 6574
- Chapter 9. Tilting complexes 8392
- 9.1. Tilting complexes and exceptional sequences 8392
- 9.2. Tilting complexes for weighted projective lines with parameters 8594
- 9.3. Branch enlargements of concealed–canonical algebras 8897
- 9.4. Tilting complexes for domestic weighted projective lines 99108
- 9.5. Tilting complexes for tubular weighted projective lines 100109
- Chapter 10. Hyperelliptic weighted projective lines 103112
- 10.1. Structure of a tilting complex on a hyperelliptic weighted projective line 103112
- 10.2. Diophantine equations 106115
- 10.3. Layered algebras 108117
- 10.4. Tame algebras derived equivalent to hyperelliptic algebras 113122
- 10.5. Tame algebras derived equivalent to t–subspace problem algebras 116125
- 10.6. Proofs of the classification results 119128
- Bibliography 133142
- Index 139148 free