Polytopes, periods, degenerations

Abstract: A lattice polytope describes a projective toric variety and a regular subdivision of the polytope describes a flat degeneration of the toric variety. It is instructive to deform the degenerating family in a way that makes the geometry non-toric and produces a more interesting real torus fibration on the fibres of the degeneration. I am going to explain a simple formula that permits the easy computation of period integrals for the deformed families. This approach to periods doesn't require any differential equations and is flexible enough to give proofs for strong results about Gross-Siebert's degenerating families obtained from wall structures. The talk is based on joint work with Bernd Siebert.

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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