Gluing Bridgeland's stability conditions and Z2-equivariant sheaves on curves

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Date

2009-06

Authors

Collins, John, 1981-

Journal Title

Journal ISSN

Volume Title

Publisher

University of Oregon

Abstract

We define and study a gluing procedure for Bridgeland stability conditions in the situation where a triangulated category has a semiorthogonal decomposition. As one application, we construct an open, contractible subset U in the stability manifold of the derived category [Special characters omitted.] of [Special characters omitted.] -equivariant coherent sheaves on a smooth curve X , associated with a degree 2 map X [arrow right] Y , where Y is another curve. In the case where X is an elliptic curve we construct an open, connected subset in the stability manifold using exceptional collections containing the subset U . We also give a new proof of the constructibility of exceptional collections on [Special characters omitted.] . This dissertation contains previously unpublished co-authored material.

Description

vi, 85 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.

Keywords

Stability conditions, Equivariant sheaves, Derived categories, Elliptic curve, Mathematics

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