Open Access
2017 Gauss maps of toric varieties
Katsuhisa Furukawa, Atsushi Ito
Tohoku Math. J. (2) 69(3): 431-454 (2017). DOI: 10.2748/tmj/1505181625


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.


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Katsuhisa Furukawa. Atsushi Ito. "Gauss maps of toric varieties." Tohoku Math. J. (2) 69 (3) 431 - 454, 2017.


Published: 2017
First available in Project Euclid: 12 September 2017

zbMATH: 06814878
MathSciNet: MR3695993
Digital Object Identifier: 10.2748/tmj/1505181625

Primary: 14M25
Secondary: 14N05

Keywords: Cayley sum , gauss map , toric variety

Rights: Copyright © 2017 Tohoku University

Vol.69 • No. 3 • 2017
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