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 discuss results which show that the classification of log symplectic pairs of pure weight is analogous to the classification of log Calabi-Yau surfaces. Time permitting, I'll discuss two classes of log symplectic pairs which are related to real hyperplane arrangements and which admit cluster type structures.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )

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Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

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