A new method in Fano geometry
Algebraic Geometry
2007-05-23 v1
Abstract
We give some bounds on the anticanonical degrees of Fano varieties with Picard number 1 and mild singularities, extending results of Koll\'ar et al. from the early 90's and improving them even in the smooth case. The proof is based on a study of positivity properties of sheaves of differential operators on ample line bundles, and avoids the use of rational curves and bend-and-break. This note is a self-contained exposition of the main ideas of math.AG/9811022
Cite
@article{arxiv.math/0001120,
title = {A new method in Fano geometry},
author = {Ziv Ran and Herb Clemens},
journal= {arXiv preprint arXiv:math/0001120},
year = {2007}
}
Comments
16 pages LaTeX; to appear in Int. Math Research Notices