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arXiv · 2311.11996

K-theoretic positivity for matroids

Christopher Eur·Matt Larson
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Abstract

Hilbert polynomials have positivity properties under favorable conditions. We establish a similar "K-theoretic positivity" for matroids. As an application, for a multiplicity-free subvariety of a product of projective spaces such that the projection onto one of the factors has birational image, we show that a transformation of its K-polynomial is Lorentzian. This partially answers a conjecture of Castillo, Cid-Ruiz, Mohammadi, and Montano. As another application, we show that the h*-vector of a simplicially positive divisor on a matroid is a Macaulay vector, affirmatively answering a question of Speyer for a new infinite family of matroids.

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Christopher Eur, Matt Larson. 2023-11-20. K-theoretic positivity for matroids. https://arxiv.org/abs/2311.11996

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