We give a sharp lower bound for the self-intersection of a nef line bundle on an irregular variety in terms of its continuous global sections and the Albanese dimension of , 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 is of maximal Albanese dimension the bound is and it is sharp.
"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