The integer decomposition property and Ehrhart unimodality for weighted projective space simplices
Benjamin Braun (University of Kentucky)
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
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
Organizers: | Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi |
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