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This is a Quantitative Study study.

October 13, 2025Open Access

Hodge theory of matroids by star subdivisions

Key Points

The proof establishes that the Chow ring of a matroid satisfies the Hard Lefschetz property.
It shows that star subdivisions can be used in decomposing the deletion operation effectively.
A combinatorial approach avoids the need for intersection cohomology or algebraic geometry.
This method simplifies understanding of Hodge Riemann relations in the context of matroids.

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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Cite This Study

Andy Hsiao (Sat,) studied this question.

synapsesocial.com/papers/68ecfebf950606aabec092a8 https://doi.org/https://doi.org/10.48550/arxiv.2509.10909

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