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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