Local multiplicativity of perverse filtrations
Abstract
Abstract Let 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 is multiplicative on each fiber if and only if is an elliptic fibration. As a consequence, we show that under certain conditions, the multiplicativity of perverse filtration associated with can be checked on each fiber. We also give an example that the existence of strongly multiplicative splitting cannot be checked locally.
Fields of Study & Subjects
Geometry and complex manifolds
Algebraic Geometry and Number Theory
Geometric Analysis and Curvature Flows
Publication details
- Journal / source
- Transactions of the London Mathematical Society
- Volume
- 13
- Issue
- 1
- Publication date
- 6 July 2026
- Language
- EN