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arXiv · 2509.10909

Hodge theory of matroids by star subdivisions

Andy Hsiao
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Abstract

It is known that the Chow ring of a matroid satisfies the Hard Lefschetz property and Hodge Riemann relations. We provide a proof of this theorem by decomposition of the deletion operation into star subdivisions at two dimensional cones. This gives a simple combinatorial proof which avoids intersection cohomology or algebraic geometry.

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Andy Hsiao. 2025-09-13. Hodge theory of matroids by star subdivisions. https://arxiv.org/abs/2509.10909

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