Holomorphic symmetric differentials and a birational characterization of abelian varieties

Ernesto C. Mistretta

Mathematische Nachrichten, 2020, vol. 293, issue 11, 2175-2186

Abstract: A generically generated vector bundle on a smooth projective variety yields a rational map to a Grassmannian, called Kodaira map. We answer a previous question, raised by the asymptotic behaviour of such maps, giving rise to a birational characterization of abelian varieties. In particular we prove that, under the conjectures of the Minimal Model Program, a smooth projective variety is birational to an abelian variety if and only if it has Kodaira dimension 0 and some symmetric power of its cotangent sheaf is generically generated by its global sections.

Date: 2020
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https://doi.org/10.1002/mana.201900102

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