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Cohomologies of tautological bundles of matroids

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arxiv 2307.04813 v3 pith:OHY44YJA submitted 2023-07-10 math.AG math.CO

Christopher Eur This is my paper · ORCID
classification math.AGmath.CO
keywords bundlescohomologiesmatroidstautologicalapplicationarrangementbest23bundle
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Tautological bundles of realizations of matroids were introduced in [BEST23] as a unifying geometric model for studying matroids. We compute the cohomologies of exterior and symmetric powers of these vector bundles, and show that they depend only on the matroid of the realization. As an application, we show that the log canonical bundle of a wonderful compactification of a hyperplane arrangement complement, in particular the moduli space of pointed rational curves, has vanishing higher cohomologies.

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