Algebraic geometry seminar: Hodge adjacency conditions for singularities, and a footnote on Deligne’s paper

Speaker: RJ Acuña (SIMIS)

Time: 2025-12-19 10:30-11:30
Location: 910, SIMIS
Zoom Meeting ID: 890 0028 4761 Passcode: SIMIS

摘要：

We prove compatibility relations between mixed Hodge numbers of k-Du Bois fibers in flat projective families and versal deformations of isolated k-Du Bois singularities. These extend the notion of polarized relations in asymptotic Hodge theory beyond the normal-crossing boundary case, and we study combinatorial properties of the resulting weak polarized relations graphs. As an example we show in the case of complete intersections of quadrics all the weak polarized relations graphs are saturated. To show the result for quadrics we find a closed form formula for the Hodge numbers of all smooth complete intersections in projective space, and complete Deligne’s proof that those Hodge numbers are unimodal.