Ordinary varieties with trivial canonical bundle are not uniruled

2020/06/08 by Patakfalvi, Zsolt, Zdanowicz, Maciej · 1 citation
#14J45 #14M25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Primary 14G17 #Secondary 14M17

paper · doi:10.48550/arxiv.2006.04692

Abstract

We prove that smooth, projective, K-trivial, weakly ordinary varieties over a perfect field of characteristic p>0 are not geometrically uniruled. We also show a singular version of our theorem, which is sharp in multiple aspects. Our work, together with Langer's results, implies that varieties of the above type have strongly semistable tangent bundles with respect to any polarization.

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• Effective characterization of ordinary abelian varieties, and beyond

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