## Kyoto Journal of Mathematics

### Strongly symmetric smooth toric varieties

#### 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.

#### Article information

Source
Kyoto J. Math., Volume 52, Number 3 (2012), 597-620.

Dates
First available in Project Euclid: 26 July 2012

https://projecteuclid.org/euclid.kjm/1343309708

Digital Object Identifier
doi:10.1215/21562261-1625208

Mathematical Reviews number (MathSciNet)
MR2959949

Zentralblatt MATH identifier
1270.14024

#### Citation

Cuntz, M.; Ren, Y.; Trautmann, G. Strongly symmetric smooth toric varieties. Kyoto J. Math. 52 (2012), no. 3, 597--620. doi:10.1215/21562261-1625208. https://projecteuclid.org/euclid.kjm/1343309708

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