Irreducible components of Toric Complete Intersections
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915421998809088 |
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| author | Zhizhin, Andrey |
| author_facet | Zhizhin, Andrey |
| contents | An equivariant linear system on a toric variety is a linear system invariant under the torus action. We study the number of irreducible components of the complete intersection of general divisors from a fixed collection of equivariant linear system on a toric variety $X$. An explicit formula for the number of components was obtained by Khovanskii in 2016 for the case $X = T^n$ over $\mathbb C$ and generalized to an algebraically closed field of arbitrary characteristic the author in 2024. Building on these results, we give a recursive formula for an arbitrary toric variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00745 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irreducible components of Toric Complete Intersections Zhizhin, Andrey Algebraic Geometry An equivariant linear system on a toric variety is a linear system invariant under the torus action. We study the number of irreducible components of the complete intersection of general divisors from a fixed collection of equivariant linear system on a toric variety $X$. An explicit formula for the number of components was obtained by Khovanskii in 2016 for the case $X = T^n$ over $\mathbb C$ and generalized to an algebraically closed field of arbitrary characteristic the author in 2024. Building on these results, we give a recursive formula for an arbitrary toric variety. |
| title | Irreducible components of Toric Complete Intersections |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2508.00745 |