Affine toric varieties with an open orbit of an $S{L}_n$ action

Abstract

We study affine toric varieties with an action of group $S{L}_n$ with a dense orbit. A characterisation in terms of $S{L}_n\times Q$-modules is given where $Q$ is a quasitorus. This characterisation is more explicitly expanded in case $n=3$. It is shown that in case $n=3$ the class group rank is not greater than $3$, however it is unbounded when $n\ge 4$.

References in corpus (1)

• Neighborly and almost neighborly configurations, and their duals