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.
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