Log symplectic pairs and mixed Hodge structures

Abstract: A log symplectic pair is a pair (X,Y) consisting of a smooth projective variety X and a divisor Y in X so that there is a non-degenerate log 2-form on X with poles along Y. I will discuss the relationship between log symplectic pairs and degenerations of hyperkaehler varieties, and how this naturally leads to a class of log symplectic pairs called log symplectic pairs of "pure weight". I will talk about common properties of cohomology rings of log symplectic pairs of pure weight and type III degenerations of hyperkaehler varieties, in particular, the fact that both have the curious hard Lefschetz' (CHL) property discovered by Hausel and Rodriguez-Villegas. Finally I will discuss partial results towards proving that in both of these cases, the CHL property is a consequence of P=W type results. Part of this is based on work with Li, Shen, and Yin.

algebraic geometry

Audience: researchers in the topic

ZAG (Zoom Algebraic Geometry) seminar

Series comments: Description: ZAG seminar

The seminar takes place on Tuesdays and Thursdays via Zoom. Zoom passwords are given via mailing list on Fridays. To join the mailing list go to the website.

If you use a calendar system, you can see the individual seminars at bit.ly/zag-seminar-calendar

Times vary to accommodate speakers time zones but times will be announced in GMT time.