Tohoku Mathematical Journal

Gauss maps of toric varieties

Katsuhisa Furukawa and Atsushi Ito

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Abstract

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

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

Dates
First available in Project Euclid: 12 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1505181625

Digital Object Identifier
doi:10.2748/tmj/1505181625

Mathematical Reviews number (MathSciNet)
MR3695993

Zentralblatt MATH identifier
06814878

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

Keywords
Gauss map toric variety Cayley sum

Citation

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


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