Tohoku Mathematical Journal

Weak del Pezzo surfaces with irregularity

Stefan SchrÖer

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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.

Article information

Source
Tohoku Math. J. (2), Volume 59, Number 2 (2007), 293-322.

Dates
First available in Project Euclid: 18 June 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1182180737

Digital Object Identifier
doi:10.2748/tmj/1182180737

Mathematical Reviews number (MathSciNet)
MR2347424

Zentralblatt MATH identifier
1135.14033

Subjects
Primary: 14J45: Fano varieties
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]

Keywords
Del Pezzo surfaces group scheme actions vanishing theorems

Citation

SchrÖer, Stefan. Weak del Pezzo surfaces with irregularity. Tohoku Math. J. (2) 59 (2007), no. 2, 293--322. doi:10.2748/tmj/1182180737. https://projecteuclid.org/euclid.tmj/1182180737


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