Holomorphic symmetric differentials and a birational characterization of abelian varieties |
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Authors: | Ernesto C Mistretta |
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Institution: | Dipartimento di Matematica, Università di Padova, Via Trieste, 63, 35121 Padova, Italy |
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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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Keywords: | abelian varieties positivity of vector bundles projective varieties |
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