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.

中文翻译：

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阿贝尔簇的全纯对称微分和双有理表征

在平滑射影变体上一般生成的向量丛产生到 Grassmannian 的有理映射，称为 Kodaira 映射。我们回答了先前由此类映射的渐近行为提出的问题，从而产生了阿贝尔变体的双有理特征。特别地，我们证明，在最小模型程序的猜想下，当且仅当它具有小平维 0 并且其余切层的某些对称幂通常由其全局部分生成时，平滑射影簇对阿贝尔簇是双有理的。