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PreprintCC BY 4.0arXiv

Automorphisms of toric varieties and Gale duality

  • Ivan Arzhantsev
  • Kirill Shakhmatov
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Abstract

We classify complete toric threefolds X such that the automorphism group Aut(X) acts on X with an open orbit whose complement does not contain a divisor. The latter condition means that for any ray ρ of the fan ΣX there is a Demazure root of ΣX associated with ρ. We also find among these varieties those X for which the group Aut(X) is transitive on the smooth locus Xreg. The classifications are based on Gale-dual interpretations of these properties.

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Cite

BibTeXRIS
BibTeX
@misc{arzhantsev2026automorphisms,
  title = {{Automorphisms of toric varieties and Gale duality}},
  author = {Ivan Arzhantsev and Kirill Shakhmatov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09051},
  eprint = {2609.09051},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09051},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Automorphisms of toric varieties and Gale duality
AU  - Ivan Arzhantsev
AU  - Kirill Shakhmatov
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09051
UR  - https://arxiv.org/abs/2609.09051
AB  - We classify complete toric threefolds X such that the automorphism group Aut(X) acts on X with an open orbit whose complement does not contain a divisor. The latter condition means that for any ray ρ of the fan Σ_X there is a Demazure root of Σ_X associated with ρ. We also find among these varieties those X for which the group Aut(X) is transitive on the smooth locus X^reg. The classifications are based on Gale-dual interpretations of these properties.
ER  -