1.

Record Nr.

UNINA9910480408003321

Autore

Meltzer Hagen

Titolo

Exceptional vector bundles, tilting sheaves, and tilting complexes for weighted projective lines / / Hagen Meltzer

Pubbl/distr/stampa

Providence, Rhode Island : , : American Mathematical Society, , 2004

©2004

ISBN

1-4704-0409-5

Descrizione fisica

1 online resource (154 p.)

Collana

Memoirs of the American Mathematical Society, , 0065-9266 ; ; Volume 171, Number 808

Disciplina

514.224

Soggetti

Vector bundles

Representations of rings (Algebra)

Homology theory

Electronic books.

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"Volume 171, Number 808 (first of 4 numbers)."

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

""Contents""; ""Abstract""; ""Chapter 1. Background""; ""Chapter 2. Summary""; ""Chapter 3. Weighted projective lines""; ""3.1. Basic notations""; ""3.2. Exceptional sheaves""; ""3.3. Perpendicular categories""; ""Chapter 4. Mutations of exceptional sequences""; ""4.1. Exceptional sequences""; ""4.2. The braid group action on the set of exceptional sequences""; ""4.3. Transitivity of the braid group action""; ""4.4. Bijections between exceptional sheaves""; ""4.5. Coprimeness of rank and degree""; ""Chapter 5. Tubular mutations""

""5.1. Mutations as derived equivalences for sheaves on weighted projective lines of genus one""""5.2. Telescopic functors""; ""5.3. Automorphisms of the derived category""; ""Chapter 6. Twisted mutations""; ""6.1. Admissible exceptional pairs""; ""6.2. Twisted mutations of admissible exceptional pairs""; ""Chapter 7. On the number of exceptional vector bundles""; ""7.1. Equations and inequalities for exceptional bundles""; ""7.2. A bound for the number of exceptional bundles of fixed rank and degree""; ""7.3. Omnipresent exceptional vector bundles""; ""Chapter 8. Tilting sheaves""

""8.1. Concealed�canonical and almost concealed�canonical algebras""""8.2. Regular components""; ""8.3. The wing decomposition



of a tilting bundle""; ""8.4. Non�regular components for concealed�canonical algebras""; ""8.5. Non�regular components for almost concealed�canonical algebras""; ""Chapter 9. Tilting complexes""; ""9.1. Tilting complexes and exceptional sequences""; ""9.2. Tilting complexes for weighted projective lines with parameters""; ""9.3. Branch enlargements of concealed�canonical algebras""; ""9.4. Tilting complexes for domestic weighted projective lines""

""9.5. Tilting complexes for tubular weighted projective lines""""Chapter 10. Hyperelliptic weighted projective lines""; ""10.1. Structure of a tilting complex on a hyperelliptic weighted projective line""; ""10.2. Diophantine equations""; ""10.3. Layered algebras""; ""10.4. Tame algebras derived equivalent to hyperelliptic algebras""; ""10.5. Tame algebras derived equivalent to t�subspace problem algebras""; ""10.6. Proofs of the classification results""; ""Bibliography""; ""Index""