Electronic ISBN:  9781470404093 
Product Code:  MEMO/171/808.E 
List Price:  $68.00 
MAA Member Price:  $61.20 
AMS Member Price:  $40.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 171; 2004; 139 ppMSC: Primary 14; 16;
This work deals with weighted projective lines, a class of noncommutative curves modelled by Geigle and Lenzing on a graded commutative sheaf theory. They play an important role in representation theory of finitedimensional 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 AuslanderReiten 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.
ReadershipGraduate students and research mathematicians interested in algebraic geometry and representations of finitedimensional 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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This work deals with weighted projective lines, a class of noncommutative curves modelled by Geigle and Lenzing on a graded commutative sheaf theory. They play an important role in representation theory of finitedimensional 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 AuslanderReiten 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.
Graduate students and research mathematicians interested in algebraic geometry and representations of finitedimensional 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