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Abstract:
Many people believe that the machinery of the derived
category is too technical, and is easily avoidable in studying singular
spaces. In this talk, we will look at three specific examples of
problems that are formidable without the derived category, and are mere
exercises once one knows basic results about perverse sheaves and
Verdier dualizing. We look at a problem on Betti numbers of Milnor
fibers for one-dimensional hypersurface singularities, a problem on
local systems on complements of hyperplane arrangements, and a problem
on Betti numbers of the complex and real links of an isolated complete
intersection singularity.
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