Log-concavity of polynomials arising from equivariant cohomology
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915049144057856 |
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| author | Cid-Ruiz, Yairon Li, Yupeng Matherne, Jacob P. |
| author_facet | Cid-Ruiz, Yairon Li, Yupeng Matherne, Jacob P. |
| contents | We study the equivariant cohomology classes of torus-equivariant subvarieties of the space of matrices. For a large class of torus actions, we prove that the polynomials representing these classes (up to suitably changing signs) are covolume polynomials in the sense of Aluffi. We study the cohomology rings of complex varieties in terms of Macaulay inverse systems over $\mathbb{Z}$. As applications, we show that under certain conditions, the Macaulay dual generator is a denormalized Lorentzian polynomial in the sense of Brändén and Huh, and we give a characteristic-free extension (over $\mathbb{Z}$) of the result of Khovanskii and Pukhlikov describing the cohomology ring of toric varieties in terms of volume polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17572 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Log-concavity of polynomials arising from equivariant cohomology Cid-Ruiz, Yairon Li, Yupeng Matherne, Jacob P. Algebraic Geometry Commutative Algebra Combinatorics 14M15, 14C15, 14C17, 13H15, 52B40 We study the equivariant cohomology classes of torus-equivariant subvarieties of the space of matrices. For a large class of torus actions, we prove that the polynomials representing these classes (up to suitably changing signs) are covolume polynomials in the sense of Aluffi. We study the cohomology rings of complex varieties in terms of Macaulay inverse systems over $\mathbb{Z}$. As applications, we show that under certain conditions, the Macaulay dual generator is a denormalized Lorentzian polynomial in the sense of Brändén and Huh, and we give a characteristic-free extension (over $\mathbb{Z}$) of the result of Khovanskii and Pukhlikov describing the cohomology ring of toric varieties in terms of volume polynomials. |
| title | Log-concavity of polynomials arising from equivariant cohomology |
| topic | Algebraic Geometry Commutative Algebra Combinatorics 14M15, 14C15, 14C17, 13H15, 52B40 |
| url | https://arxiv.org/abs/2411.17572 |