A new method in Fano geometry

Details A new method in Fano geometry A new method in Fano geometry

2000-01-23

arxiv.org/abs/math/0001120v1

Mathematics

Algebraic Geometry

16 pages LaTeX; to appear in Int. Math Research Notices

Scientific paper

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

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