K-theoretic positivity for matroids
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917779676856320 |
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| author | Eur, Christopher Larson, Matt |
| author_facet | Eur, Christopher Larson, Matt |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11996 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | K-theoretic positivity for matroids Eur, Christopher Larson, Matt Algebraic Geometry Combinatorics 14M99 05B35 52C35 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. |
| title | K-theoretic positivity for matroids |
| topic | Algebraic Geometry Combinatorics 14M99 05B35 52C35 |
| url | https://arxiv.org/abs/2311.11996 |