Algebraic Geometry Seminar

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Hodge symmetries of singular varieties

Speaker: Sung Gi Park, Princeton

Location: Warren Weaver Hall 512

Date: Tuesday, February 25, 2025, 5 p.m.

Synopsis:

The Hodge diamond of a smooth projective complex variety exhibits fundamental symmetries, arising from Poincaré duality and the purity of Hodge structures. In the case of a singular projective variety, the complexity of the singularities is closely related to the symmetries of the analogous Hodge–Du Bois diamond. For example, the failure of the first nontrivial Poincaré duality is reflected in the defect of factoriality. Based on joint work with Mihnea Popa, I will discuss how local and global conditions on singularities influence the topology of algebraic varieties.