Fano varieties with small non-klt locus
Algebraic Geometry
2017-10-24 v2
Abstract
Let X be a Fano variety of index k such that the non-klt locus Nklt(X) is not empty. We prove that Nklt(X) has dimension at least k-1 and equality holds if and only if Nklt(X) is a linear projective space P^{k-1}. In this case X has lc singularities and is a generalised cone with Nklt(X) as vertex. If X has lc singularities and Nklt(X) has dimension k we describe the non-klt locus and the global geometry of X. Moreover, we construct examples to show that all the classification results are effective.
Keywords
Cite
@article{arxiv.1309.5342,
title = {Fano varieties with small non-klt locus},
author = {Mauro C. Beltrametti and Andreas Höring and Carla Novelli},
journal= {arXiv preprint arXiv:1309.5342},
year = {2017}
}
Comments
20 pages, changed metadata