The antiprism triangulation

Abstract: The antiprism triangulation provides a natural way to subdivide a simplicial complex $\Delta$, similar to barycentric subdivision, which appeared independently in combinatorial algebraic topology and computer science. It can be defined as the simplicial complex of chains of multi-pointed faces of $\Delta$ from a combinatorial point of view, and by successively applying the antiprism construction, or balanced stellar subdivisions, on the faces of $\Delta$ from a geometric point of view. In this talk, we will study enumerative invariants associated to this triangulation, such as the transformation of the $h$-vector of $\Delta$ under antiprism triangulation, the local $h$-vector, and algebraic properties of its Stanley--Reisner ring. Among other results, it is shown that the $h$-polynomial of the antiprism triangulation of a simplex is real-rooted and that the antiprism triangulation of $\Delta$ has the almost strong Lefschetz property over $\mathbb{R}$ for every shellable complex $\Delta$.

I will make the talk as self-contained as possible, and assume no previous knowledge of combinatorics of subdivisions. This is joint work with Christos Athanasiadis and Jan-Marten Brunink.

commutative algebra

Audience: researchers in the topic

Fellowship of the Ring

Series comments: Description: National Commutative Algebra Seminar

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