The local perverse filtration on fibers of a Hilbert scheme map is multiplicative on all fibers exactly when the underlying surface fibration is elliptic.
Boalch, Simply-laced isomonodromy systems , Publ
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Local multiplicativity of perverse filtrations
The local perverse filtration on fibers of a Hilbert scheme map is multiplicative on all fibers exactly when the underlying surface fibration is elliptic.