15 February 2015 Generalized Clifford–Severi inequality and the volume of irregular varieties
Miguel A. Barja
Duke Math. J. 164(3): 541-568 (15 February 2015). DOI: 10.1215/00127094-2871306


We give a sharp lower bound for the self-intersection 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 fibered irregular varieties. As a by-product we obtain a lower bound for the volume of irregular varieties; when X is of maximal Albanese dimension the bound is vol(X)2n!χ(ωX) and it is sharp.


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Miguel A. Barja. "Generalized Clifford–Severi inequality and the volume of irregular varieties." Duke Math. J. 164 (3) 541 - 568, 15 February 2015. https://doi.org/10.1215/00127094-2871306


Published: 15 February 2015
First available in Project Euclid: 17 February 2015

zbMATH: 06422600
MathSciNet: MR3314480
Digital Object Identifier: 10.1215/00127094-2871306

Primary: 14J0
Secondary: 14J29 , 14J30 , 14J35

Keywords: continuous system , irregular variety , nef line bundle , Severi inequality

Rights: Copyright © 2015 Duke University Press

Vol.164 • No. 3 • 15 February 2015
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