On a special class of simplicial toric varieties

Abstract

We show that for all $n\ge 3$ and all primes $p$ there are infinitely many simplicial toric varieties of codimension $n$ in the $2n$-dimensional affine space whose minimum number of defining equations is equal to $n$ in characteristic $p$, and lies between $2n-2$ and $2n$ in all other characteristics. In particular, these are new examples of varieties which are set-theoretic complete intersections only in one positive characteristic.\newline Moreover, we show that the minimum number of binomial equations which define these varieties in all characteristics is 4 for $n=3$ and $2n-2+\left(\genfrac{}{}{0ex}{}{n-2}{2}\right)$ whenever $n\ge 4$.

Cited by in corpus (3)

• On simplicial toric varieties of codimension 2
• On binomial set-theoretic complete intersections in characteristic p
• Specializations of multigradings and the arithmetical rank of lattice ideals