Topology of Lagrangian fibrations and $P=W$ phenomena on irreducible symplectic varieties – Camilla Felisetti (Università di Trento)

Venue

Dipartimento di Matematica, Aula Magna.

Abstract

Irreducible holomorphic symplectic (IHS) varieties can be thought as a generalization of hyperkähler manifolds allowing singularities. Among them we can find for example moduli spaces of sheaves on $K3$ and abelian surfaces, which have been recently shown to play a crucial role in nonabelian Hodge theory. After recalling the main features of IHS varieties, I will present several results concerning their intersection cohomology and the perverse filtration associated with a Lagrangian fibration, establishing a compact analogue of the celebrated $P=W$ conjecture by de Cataldo, Hausel and Migliorini for varieties which admit a symplectic resolution. The talk is based on joint works with Mirko Mauri, Junliang Shen and Qizheng Yin.

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