Tohoku Mathematical Journal
2017
September
SECOND SERIES VOL. 69, NO. 3

Tohoku Math. J.
69 (2017), 431-454

Title GAUSS MAPS OF TORIC VARIETIES

Author Katsuhisa Furukawa and Atsushi Ito

(Received May 7, 2015, revised September 24, 2015)
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.

Mathematics Subject Classification. Primary 14M25; Secondary 14N05.
Key words and phrases. Gauss map, toric variety, Cayley sum.

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