Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 69, Number 3 (2017), 431-454.
Gauss maps of toric varieties
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.
Tohoku Math. J. (2), Volume 69, Number 3 (2017), 431-454.
First available in Project Euclid: 12 September 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Secondary: 14N05: Projective techniques [See also 51N35]
Furukawa, Katsuhisa; Ito, Atsushi. Gauss maps of toric varieties. Tohoku Math. J. (2) 69 (2017), no. 3, 431--454. doi:10.2748/tmj/1505181625. https://projecteuclid.org/euclid.tmj/1505181625