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Holomorphic symmetric differentials and a birational characterization of abelian varieties
Author(s) -
Mistretta Ernesto C.
Publication year - 2020
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201900102
Subject(s) - mathematics , kodaira dimension , abelian group , pure mathematics , cotangent bundle , projective variety , sheaf , variety (cybernetics) , abelian variety , birational geometry , vector bundle , grassmannian , dimension (graph theory) , algebra over a field , trigonometric functions , geometry , statistics
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.