Title: Linearity Properties of Degenerate Holomorphic 1-forms
Speaker: 郝峰（山东大学）
Time: Wednesday, March 25, 2026, 14:00--15:00
Venue: Room 315, Gewu Building
Abstract:
On a smooth complex projective variety, the generic vanishing theory tells us that the sets of degenerate holomorphic 1-forms coming from the cohomology jump loci are finite unions of subvector spaces in the space of holomorphic 1-forms. This linearity property comes essentially from the Hodge theoretic property of the variety. It was expected that the sets of degenerate holomorphic 1-forms (not necessarily coming from cohomology jump loci) on a smooth projective subvariety of an abelian variety also have the above linearity property. In this falk. I will discuss some backgrounds and related results on the some (linearity) properties of degenerate holomorphic 1-forms. For the above expectation, I will also give a counterexample of a subvariety of an abelian variety which does not satisfy the linearity property. This is a jointed work with Jiabin Du and Zichang Wang.
