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.
Original language | English |
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Pages (from-to) | 431-454 |
Number of pages | 24 |
Journal | Tohoku Mathematical Journal |
Volume | 69 |
Issue number | 3 |
DOIs | |
Publication status | Published - Sep 2017 |
Externally published | Yes |
Keywords
- Cayley sum
- Gauss map
- Toric variety
ASJC Scopus subject areas
- Mathematics(all)