Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.641936
Title: Fourier-Mukai transforms for surfaces and moduli spaces of stable sheaves
Author: Bridgeland, Tom
Awarding Body: University of Edinburgh
Current Institution: University of Edinburgh
Date of Award: 2002
Availability of Full Text:
Access from EThOS:
Full text unavailable from EThOS. Please try the link below.
Access from Institution:
Abstract:
In this thesis we study Fourier-Mukai transforms for complex projective surfaces. Extending work of A.I. Bondal and D.O. Orlov, we prove a theorem giving necessary and sufficient conditions for a functor between the derived categories of sheaves on two smooth projective varieties to be an equivalence of categories, and use it to construct examples of Fourier-Mukai transforms for surfaces. In particular we construct new transforms for elliptic surfaces and quotient surfaces. This enables us to identify all pairs of complex projective surfaces having equivalent derived categories of sheaves. We also derive some general properties of Fourier-Mukai transforms, and gives examples of their use. The main applications are to the study of moduli spaces of stable sheaves. In particular we identify many such moduli spaces on elliptic surfaces, generalising results of R. Friedman.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.641936  DOI: Not available
Share: