On characterization of toric varieties

Ilya Karzhemanov

On characterization of toric varieties

Algebraic Geometry 2026-02-12 v11

Authors: Ilya Karzhemanov

Abstract

We study the conjecture due to V.\,V. Shokurov on characterization of toric varieties. We also consider one generalization of this conjecture. It is shown that none of the characterizations holds true in dimension $\ge 3$ . Some weaker versions of the conjecture(s) are verified.

Keywords

toric varieties conjectures and proofs

Cite

@article{arxiv.1306.4131,
  title  = {On characterization of toric varieties},
  author = {Ilya Karzhemanov},
  journal= {arXiv preprint arXiv:1306.4131},
  year   = {2026}
}

Comments

14 pages, 1 figure; minor details to the proof of Lemma 4.4 are added; the surface Y in subsection A.1 is modified and the fact that Y is not the plane is proved by computation of its Makar-Limanov invariant (one more reference added)

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