English

Canonical divisors on T-varieties

Algebraic Geometry 2010-12-16 v2

Abstract

Generalising toric geometry we study compact varieties admitting lower dimensional torus actions. In particular we describe divisors on them in terms of convex geometry and give a criterion for their ampleness. These results may be used to study Fano varieties with small torus actions. As a first result we classify log del Pezzo C*-surfaces of Picard number 1 and Gorenstein index less than 4. In further examples we show how classification might work in higher dimensions and we give explicit descriptions of some equivariant smoothings of Fano threefolds.

Keywords

Cite

@article{arxiv.0811.0626,
  title  = {Canonical divisors on T-varieties},
  author = {Hendrik Süß},
  journal= {arXiv preprint arXiv:0811.0626},
  year   = {2010}
}

Comments

22 pages, 5 figures; v2: references updated; minor corrections; new remark 4.9. concerning relations to arXiv:1012.0240

R2 v1 2026-06-21T11:38:15.697Z