The Weight Filtration on the Constant Sheaf on a Parameterized Space

On a complex analytic space where the shifted constant sheaf is perverse, it is known that it underlies a mixed Hodge module whose weight-graded piece is isomorphic to the intersection cohomology complex. In this paper, we identify this weight-graded piece in the case of parameterized spaces using the comparison complex—a perverse sheaf naturally defined on such spaces. For parameterized surfaces, we fully determine the remaining terms in the weight filtration and show that the filtration is a local topological invariant. These examples arise naturally as images of finitely determined map germs or affine toric surfaces, and connect with a conjecture of Lê Dũng Tráng on the equisingularity of parameterized surfaces.

arXiv:1811.04328 [math.AG]