Gauss maps of toric varieties

Katsuhisa Furukawa, Atsushi Ito

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)431-454
Number of pages24
JournalTohoku Mathematical Journal
Volume69
Issue number3
DOIs
Publication statusPublished - Sep 2017
Externally publishedYes

Keywords

  • Cayley sum
  • Gauss map
  • Toric variety

ASJC Scopus subject areas

  • Mathematics(all)

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