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A new method in Fano geometry

Ziv Ran·Herb Clemens
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Abstract

We give some bounds on the anticanonical degrees of Fano varieties with Picard number 1 and mild singularities, extending results of Kollár 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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Ziv Ran, Herb Clemens. 2000-01-23. A new method in Fano geometry. https://arxiv.org/abs/math/0001120

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