Regular del Pezzo surfaces with irregularity
arXiv:1304.5555
Abstract
We construct the first examples of regular del Pezzo surfaces for which the irregularity (i.e. the dimension of the first cohomology group of the structure sheaf) is nonzero. We also find a restriction on the integer pairs that are possible as the anti-canonical degree and irregularity of such a surface.
23 pages, 1 figure (on page 2)