Effective bounds on ampleness of cotangent bundles

Abstract

We prove that a general complete intersection of dimension $n$, codimension $c$ and type $d_1,\dots ,d_c$ in ${\mathbb{P}}^N$ has ample cotangent bundle if $c\ge 2n-2$ and the $d_i$'s are all greater than a bound that is $O(1)$ in $N$ and quadratic in $n$. This degree bound substantially improves the currently best-known super-exponential bound in $N$ by Deng, although our result does not address the case $n\le c<2n-2$.

Uses a result of Darondeau to improve the bounds