The integer decomposition property and Ehrhart unimodality for weighted projective space simplices

Benjamin Braun (University of Kentucky)

30-Jul-2020, 14:00-15:00 (4 years ago)

Abstract: We consider lattice simplices corresponding to weighted projective spaces where one of the weights is $1$. We study the integer decomposition property and Ehrhart unimodality for such simplices by focusing on restrictions regarding the multiplicity of each weight. We introduce a necessary condition for when a simplex satisfies the integer decomposition property, and classify those simplices that satisfy it in the case where there are no more than three distinct weights. We also introduce the notion of reflexive stabilizations of a simpex of this type, and show that higher-order reflexive stabilizations fail to be Ehrhart unimodal and fail to have the integer decomposition property. This is joint work with Robert Davis, Morgan Lane, and Liam Solus.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )


Online Nottingham algebraic geometry seminar

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Organizers: Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi
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