arXiv 1303.30452013-03math.AG

Generalized Clifford-Severi Inequality and the Volume of Irregular Varieties

Miguel A. Barja

备注：: Final version, accepted for publication at Duke Math. J. Some typos corrected and new references added. Proof of Corollary B clarified. Exposition and proof of $5.2 simplified. Minor other changes in exposition
发表信息：: Duke Math. J. 164, no. 3 (2015), 541-568
DOI：: 10.1215/00127094-2871306

英文摘要：

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 $Vol(X) \geq 2 n! χω_X$ and it is sharp.

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