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arXiv · 1303.3045

Generalized Clifford-Severi Inequality and the Volume of Irregular Varieties

Miguel A. Barja
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Abstract

We give a sharp lower bound for the selfintersection of a nef line bundle $L$ on an irregular variety $X$ in terms of its continuous global sections and the Albanese dimension of $X$, which we call the Generalized Clifford-Severi inequality. We also extend the result to nef vector bundles and give a slope inequality for fibred irregular varieties. As a byproduct we obtain a lower bound for the volume of irregular varieties; when $X$ is of maximal Albanese dimension the bound is $Vol(X) \geq 2 n! \chi\omega_X$ and it is sharp.

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Miguel A. Barja. 2013-03-12. Generalized Clifford-Severi Inequality and the Volume of Irregular Varieties. https://doi.org/10.1215/00127094-2871306

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