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Combinatorics of Toric Arrangements

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arxiv 1710.00409 v2 pith:EKL34UHP submitted 2017-10-01 math.AT math.CO

Roberto Pagaria This is my paper · ORCID
classification math.ATmath.CO
keywords toricarrangementsalgebracohomologyconditionsgivemodelorlik-solomon
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In this paper we build an Orlik-Solomon model for the canonical gradation of the cohomology algebra with integer coefficients of the complement of a toric arrangement. We give some results on the uniqueness of the representation of arithmetic matroids, in order to discuss how the Orlik-Solomon model depends on the poset of layers. The analysis of discriminantal toric arrangements permits us to isolate certain conditions under which two toric arrangements have diffeomorphic complements. We also give combinatorial conditions determining whether the cohomology algebra is generated in degree one.

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  1. Representations of torsion-free arithmetic matroids

    math.CO 2019-08 conditional novelty 7.0 of 10

    A new reduction and signed Hermite normal form let every representation of a torsion-free arithmetic matroid be computed up to equivalence, yielding a sharpened upper bound and counterexamples to two shellability conjectures.

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