A characterization of ordinary abelian varieties by the Frobenius push-forward of the structure sheaf II

Abstract

In this paper, we prove that a smooth projective variety $X$ of characteristic $p>0$ is an ordinary abelian variety if and only if $K_X$ is pseudo-effective and $F_{\ast }^e{\mathcal{O}}_X$ splits into a direct sum of line bundles for an integer $e$ with $p^e>2$.

10 pages, v2: Abstract and Sections 3-5 shortened, Introduction revised, the statements of Theorem 1.3, Proposition 3.2 and Lemma 5.3 simplified, Corollary 1.4 moved to Remark 5.6, typos corrected

References in corpus (5)

• Direct images of bundles under Frobenius morphisms
• Arithmetically Cohen-Macaulay Bundles on complete intersection varieties of sufficiently high multidegree
• A characterization of toric varieties in characteristic p
• Frobenius morphism and semi-stable bundles
• On the height of Calabi-Yau varieties in positive characteristic

Cited by in corpus (1)

• A remark on Ulrich and ACM bundles