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arXiv · 1810.07666

Effective bounds on ampleness of cotangent bundles

Izzet Coskun·Eric Riedl
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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 $c \geq 2n-2$ 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 $n \leq c < 2n-2$.

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Izzet Coskun, Eric Riedl. 2018-10-17. Effective bounds on ampleness of cotangent bundles. https://doi.org/10.1112/blms.12322

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