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arXiv · 1812.10058

Affine toric varieties with an open orbit of an $SL_n$ action

Nikita Medved
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Abstract

We study affine toric varieties with an action of group $SL_n$ with a dense orbit. A characterisation in terms of $SL_n \times Q$-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 $n\geq 4$.

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Nikita Medved. 2018-12-25. Affine toric varieties with an open orbit of an $SL_n$ action. https://arxiv.org/abs/1812.10058

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