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Shellability for toric arrangements

Time: Wed 2019-03-06 10.15

Location: Room 3418, Lindstedtsvägen 25. Department of Mathematics, KTH

Lecturer: Ivan Martino

Abstract: Arrangements of codimension one subtori in a torus have been a fruitful topic of research since Looijenga (1993) used them to compute Poincare'–Serre polynomials of certain moduli spaces of curves.
In the last decade, a series of works have set about exploring the combinatorics and geometry of toric arrangements, much of the motivation being to obtain analogs to results in the longer-standing theory of hyperplane arrangements (for instance, the works of Branden, D’Adderio, Delucchi, and Moci). 

What appears to be 'matroidal' on the side of hyperplane arrangements is 'Z-matroidal' on the side of toric arrangements. For instance, the role of the independent simplicial complex is taken by the poset of torsions, introduced recently by the speaker and inspired by a couple of articles in the literature (mainly, by Moci and Zaslavsky).

In this talk, I will define matroids over the integers and the poset of torsion for a realizable Z-matroid. I am going to show several interesting combinatorial and algebraic properties the poset of torsion associated to a Z-matroid. For example, as the title suggests, the poset of torsion admits a shellable order of the facets.