2000/01/23 by Ziv Ran, Ran, Ziv, Herb Clemens +1
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory #Nonlinear Waves and Solitons #math.AG #msc:14j45
paper · pdf · doi:10.48550/arxiv.math/0001120
16 pages LaTeX; to appear in Int. Math Research Notices
arxiv created 2000/01/23 · arxiv updated 2009/11/30
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