Weak del Pezzo surfaces with irregularity

Details Weak del Pezzo surfaces with irregularity Weak del Pezzo surfaces with irregularity

2005-12-07

arxiv.org/abs/math/0512153v2

Mathematics

Algebraic Geometry

32 pages, minor changes, to appear in Tohoku Math. J

Scientific paper

I construct normal del Pezzo surfaces, and regular weak del Pezzo surfaces as well, with positive irregularity q>0. Such things can happen only over nonperfect fields. The surfaces in question are twisted forms of nonnormal del Pezzo surfaces, which were classified by Reid. The twisting is with respect to the flat topology and infinitesimal group scheme actions. The twisted surfaces appear as generic fibers for Fano--Mori contractions on certain threefolds with only canonical singularities.

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