Tohoku Mathematical Journal

Gauss maps of toric varieties

Katsuhisa Furukawa and Atsushi Ito

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We investigate Gauss maps of (not necessarily normal) projective toric varieties over an algebraically closed field of arbitrary characteristic. The main results are as follows: (1) The structure of the Gauss map of a toric variety is described in terms of combinatorics in any characteristic. (2) We give a developability criterion in the toric case. In particular, we show that any toric variety whose Gauss map is degenerate must be the join of some toric varieties in characteristic zero. (3) As applications, we provide two constructions of toric varieties whose Gauss maps have some given data (e.g., fibers, images) in positive characteristic.

Article information

Tohoku Math. J. (2), Volume 69, Number 3 (2017), 431-454.

First available in Project Euclid: 12 September 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Secondary: 14N05: Projective techniques [See also 51N35]

Gauss map toric variety Cayley sum


Furukawa, Katsuhisa; Ito, Atsushi. Gauss maps of toric varieties. Tohoku Math. J. (2) 69 (2017), no. 3, 431--454. doi:10.2748/tmj/1505181625.

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