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Hyperplane Arrangements and Compactifications of Vector Groups

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arxiv 2209.00052 v2 pith:K27CLWLF submitted 2022-08-31 math.AG math.CO

Colin Crowley This is my paper · ORCID
classification math.AGmath.CO
keywords varietiescompactificationsarrangementshyperplaneschubertthemtheoryaffine
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Schubert varieties of hyperplane arrangements, also known as matroid Schubert varieties, play an essential role in the proof of the Dowling-Wilson conjecture and in Kazhdan-Lusztig theory for matroids. We study these varieties as equivariant compactifications of affine spaces, and give necessary and sufficient conditions to characterize them. We also generalize the theory to include partial compactifications and morphisms between them. Our results resemble the correspondence between toric varieties and polyhedral fans.

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  1. Wonderful Compactification of a Cartan Subalgebra of a Semisimple Lie Algebra

    math.RT 2024-11 conditional novelty 6.0 of 10

    A Cartan subalgebra admits a wonderful compactification whose boundary components, affine paving, and cohomology are governed by the root system and its Coxeter arrangement.

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