Strongly symmetric smooth toric varieties

TL;DR

This paper classifies strongly symmetric smooth toric varieties, characterized by crystallographic hyperplane arrangements, establishing their projectivity and describing related toric arrangements.

Contribution

It provides a complete classification of strongly symmetric smooth toric varieties based on crystallographic arrangements and explores their projective properties.

Findings

Classification of strongly symmetric smooth toric varieties

Connection between smoothness and crystallographic arrangements

Description of associated toric arrangements

Abstract

We investigate toric varieties defined by arrangements of hyperplanes and call them strongly symmetric. The smoothness of such a toric variety translates to the fact that the arrangement is crystallographic. As a result, we obtain a complete classification of this class of toric varieties. Further, we show that these varieties are projective and describe associated toric arrangements in these varieties.