On binomial set-theoretic complete intersections in characteristic p

TL;DR

This paper investigates when simplicial toric varieties of codimension 2 are set-theoretic complete intersections on binomials in characteristic p, revealing that this property is either universal, absent, or exclusive to a single prime p.

Contribution

It establishes arithmetic conditions on affine semigroups that determine the characteristic p behavior of set-theoretic complete intersections in simplicial toric varieties of codimension 2.

Findings

The property holds for all primes p, no primes p, or exactly one prime p.

Provides criteria based on affine semigroup arithmetic conditions.

Clarifies the characteristic p dependence of binomial set-theoretic complete intersections.

Abstract

Using aritmethic conditions on affine semigroups we prove that for a simplicial toric variety of codimension 2 the property of being a set-theoretic complete intersection on binomials in characteristic $p$ holds either for all primes $p$, or for no prime $p$, or for exactly one prime $p$.