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arXiv · 2508.00745

Irreducible components of Toric Complete Intersections

Andrey Zhizhin
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Abstract

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.

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Andrey Zhizhin. 2025-08-01. Irreducible components of Toric Complete Intersections. https://arxiv.org/abs/2508.00745

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