Local multiplicativity of perverse filtrations

Abstract

Let $f:S\to C$ be a proper surjective morphism from a smooth Kähler surface to a smooth curve. We show that the local perverse filtration associated with the induced map $S^{[n]}\to C^{(n)}$ is multiplicative on each fiber if and only if $f$ is an elliptic fibration.

13 pages, all comments are welcome!