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arXiv · 2303.09894

Varieties in positive characteristic with numerically flat log cotangent bundle

Sho Ejiri·Shou Yoshikawa
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Abstract

In this paper, we prove that a smooth projective globally $F$-split variety with numerically flat tangent bundle is an \'etale quotient of an ordinary abelian variety. We also show its logarithmic analog, which contains a characterization of toric varieties. We further prove that, without assumption of global $F$-splitting, a smooth projective separably rationally connected variety of arbitrary characteristic with numerically flat log cotangent bundle is a toric variety.

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Sho Ejiri, Shou Yoshikawa. 2023-03-17. Varieties in positive characteristic with numerically flat log cotangent bundle. https://arxiv.org/abs/2303.09894

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