Isolated hypersurface singularities as noncommutative spaces                                                                                   
-- Tobias Dyckerhoff, November 20, 2009
                                       
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Eisenbud's category MF of matrix factorizations is a
differential graded category associated to the local germ X of
a algebraic hypersurface. If the hypersurface is regular, then
this category is trivial which, in general, allows us to think
of MF as an invariant of the singularity of X.  Noncommutative
geometry based on dg categories allows us to interpret MF as
the category of sheaves on a noncommutative space. We will
explain how to obtain various properties (smoothness,
properness) and invariants (de Rham cohomology, Hodge
cohomology) of this space.