Rational points of fixed denominator in real toric arrangements
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914326552510464 |
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| author | Hanlon, Andrew Painter, Davis |
| author_facet | Hanlon, Andrew Painter, Davis |
| contents | We give a sufficient condition on a positive integer $m$ for every stratum of a given real toric hyperplane arrangement to contain a rational point of denominator $m$. As a consequence, we give a sufficient condition on $m$ for the degree $m$ Frobenius pushforward of the structure sheaf on a smooth toric variety to contain all possible summands in the Picard group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07164 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational points of fixed denominator in real toric arrangements Hanlon, Andrew Painter, Davis Combinatorics Algebraic Geometry 52C35, 05E14, 14M25 We give a sufficient condition on a positive integer $m$ for every stratum of a given real toric hyperplane arrangement to contain a rational point of denominator $m$. As a consequence, we give a sufficient condition on $m$ for the degree $m$ Frobenius pushforward of the structure sheaf on a smooth toric variety to contain all possible summands in the Picard group. |
| title | Rational points of fixed denominator in real toric arrangements |
| topic | Combinatorics Algebraic Geometry 52C35, 05E14, 14M25 |
| url | https://arxiv.org/abs/2408.07164 |