Grassmannian twists on derived categories of coherent sheaves
Author(s)
Donovan, William Ross Goodchild
Type
Thesis
Abstract
We construct new examples of derived autoequivalences, for a family
of higher-dimensional Calabi-Yau varieties. Specifically, we define endo-
functors of the bounded derived categories of coherent sheaves associated
to varieties arising as the total spaces of certain natural vector bundles
over complex Grassmannians. These functors are defined using Fourier-
Mukai techniques, and naturally generalize the Seidel-Thomas spherical
twist for analogous bundles over complex projective spaces. We prove
that they are autoequivalences.
We also give a discussion of the motivation for this construction, which
comes from homological mirror symmetry.
of higher-dimensional Calabi-Yau varieties. Specifically, we define endo-
functors of the bounded derived categories of coherent sheaves associated
to varieties arising as the total spaces of certain natural vector bundles
over complex Grassmannians. These functors are defined using Fourier-
Mukai techniques, and naturally generalize the Seidel-Thomas spherical
twist for analogous bundles over complex projective spaces. We prove
that they are autoequivalences.
We also give a discussion of the motivation for this construction, which
comes from homological mirror symmetry.
Date Issued
2011
Date Awarded
2011-11
Copyright Statement
Attribution NoDerivatives 4.0 International Licence (CC BY-ND)
Advisor
Segal, Edward
Thomas, Richard
Sponsor
EPSRC
Creator
Donovan, William Ross Goodchild
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)