Date of Award
Spring 2010
Degree Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Graduate Group
Mathematics
First Advisor
Tony Pantev
Abstract
We study the category of matrix factorizations associated to the germ of an isolated hypersurface singularity. This category is shown to admit a compact generator which is given by the stabilization of the residue field. We deduce a quasi-equivalence between the category of matrix factorizations and the dg derived category of an explicitly computable dg algebra. Building on this result, we employ a variant of Toen's derived Morita theory to identify continuous functors between matrix factorization categories as integral transforms. This enables us to calculate the Hochschild chain and cochain complexes of these categories. Finally, we give interpretations of the results of this thesis in terms of noncommutative geometry based on dg categories.
Recommended Citation
Dyckerhoff, Tobias, "Isolated Hypersurface Singularities as Noncommutative Spaces" (2010). Publicly Accessible Penn Dissertations. 111.
https://repository.upenn.edu/edissertations/111