arXiv subjects

Andrey Zhizhin

Publications and source records attributed to Andrey Zhizhin.

2 recordsLinked to original sources

arXiv2025

Irreducible components of Toric Complete Intersections

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.

math.AG↗

arXiv2024

Irreducibility of toric complete intersections

We develop an approach to study the irreducibility of generic complete intersections in the algebraic torus defined by equations with fixed monomials and fixed linear relations on coefficients. Using our approach we generalize the irreducibility theorems of Khovanskii to fields of arbitrary characteristic. Also we get a combinatorial sufficient conditions for irreducibility of engineered complete intersections. As an application we give a combinatorial condition of irreducibility for some critical loci and Thom-Bordmann strata: $f = f'_x = 0$, $f'_x = f'_y = 0$, $f = f'_x = f'_{xx} = 0$, where f is a generic Laurent polynomial with a prescribed monomial set.

math.AG↗