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February 10, 2020
Monday, February 10
Geometry and Combinatorics
Time: 15:30
Speaker: Brian Hepler (University of Wisconsin)
Title: "The Weight Filtration on the Constant Sheaf on a Parameterized Surface"
Room: MC 108

Abstract: \def\Q{\mathbb Q} On an n-dimensional locally reduced complex analytic space X on which the shifted constant sheaf \Q_X[n] is perverse, it is well-known that, locally, \Q_X[n] underlies a mixed Hodge module of weight <= n on X, with weight n graded piece isomorphic to the intersection cohomology complex IC_X with constant \Q coefficients. In this paper, we identify the weight (n-1) graded piece Gr_{n-1}^W \Q_X[n] in the case where X is a “parameterized space", using the comparison complex, a perverse sheaf naturally defined on any space for which the shifted constant sheaf \Q_X[n] is perverse.Â