Algebraic and Arithmetic Geometry Seminar

Topology of Lagrangian fibrations and $P=W$ phenomena on irreducible symplectic varieties

by Camilla Felisetti (Università di Trento)

Aula Magna (Dipartimento di Matematica)

Aula Magna

Dipartimento di Matematica


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.