Equivariant Euler characteristics on permutohedral varieties
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912647152140288 |
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| author | Galgano, Vincenzo Keneshlou, Hanieh Michalek, Mateusz |
| author_facet | Galgano, Vincenzo Keneshlou, Hanieh Michalek, Mateusz |
| contents | By the work of J.Huh, one can interpret binomial coefficients as a solution to an intersection problem on a permutohedral variety $X_E$. Applying Hirzebruch-Riemann-Roch, this intersection problem is equivalent to computing Euler characteristic of a specific element of $K$-theory of $X_E$. This element has a natural lifting to equivariant $K$-theory and thus the Euler characteristic may be upgraded to a Laurent polynomial. We provide and implement three different approaches, in particular a recursive one, to computing these polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_04598 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Equivariant Euler characteristics on permutohedral varieties Galgano, Vincenzo Keneshlou, Hanieh Michalek, Mateusz Algebraic Geometry By the work of J.Huh, one can interpret binomial coefficients as a solution to an intersection problem on a permutohedral variety $X_E$. Applying Hirzebruch-Riemann-Roch, this intersection problem is equivalent to computing Euler characteristic of a specific element of $K$-theory of $X_E$. This element has a natural lifting to equivariant $K$-theory and thus the Euler characteristic may be upgraded to a Laurent polynomial. We provide and implement three different approaches, in particular a recursive one, to computing these polynomials. |
| title | Equivariant Euler characteristics on permutohedral varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2302.04598 |