Kyoto Journal of Mathematics

Strongly symmetric smooth toric varieties

M. Cuntz, Y. Ren, and G. Trautmann

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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.

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

First available in Project Euclid: 26 July 2012

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Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15] 52C35: Arrangements of points, flats, hyperplanes [See also 32S22] 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx] 14M25: Toric varieties, Newton polyhedra [See also 52B20]


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.

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