On monodromies of a degeneration of irreducible symplectic K\"ahler manifolds

TL;DR

This paper investigates the monodromy operators in degenerations of irreducible symplectic Kähler manifolds, establishing a lower bound on their unipotency degree related to the manifold's dimension.

Contribution

It provides a new lower bound on the unipotency of monodromy operators in degenerations of irreducible symplectic manifolds, linking it to the manifold's dimension.

Findings

Unipotency of monodromy on middle cohomology is at least half the dimension.

Monodromy operators are studied in the context of good degenerations.

Results contribute to understanding the degeneration behavior of symplectic manifolds.

Abstract

We study the monodromy operators on the betti cohomologies associated to a good degeneration of irreducible symplectic manifold and we show that the unipotency of the monodromy operator on the middle cohomology is at least the half of the dimension.