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Holomorphic symmetric differentials and a birational characterization of abelian varieties

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  • Ernesto C. Mistretta

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.

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  • Ernesto C. Mistretta, 2020. "Holomorphic symmetric differentials and a birational characterization of abelian varieties," Mathematische Nachrichten, Wiley Blackwell, vol. 293(11), pages 2175-2186, November.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:11:p:2175-2186
    DOI: 10.1002/mana.201900102
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