Tohoku Mathematical Journal
2007
June
SECOND SERIES VOL. 59, NO. 2

Tohoku Math. J.
59 (2007), 293-322

Title WEAK DEL PEZZO SURFACES WITH IRREGULARITY

Author Stefan Schröer

(Received January 16, 2006, revised January 15, 2007)
Abstract. We construct normal del Pezzo surfaces, and regular weak del Pezzo surfaces as well, with positive irregularity $q>0$. This 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.

2000 Mathematics Subject Classification. Primary 14J45; Secondary 14L30.
Key words and phrases. Del Pezzo surfaces, group scheme actions, vanishing theorems.

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