Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 59, Number 2 (2007), 293-322.
Weak del Pezzo surfaces with irregularity
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.
Tohoku Math. J. (2), Volume 59, Number 2 (2007), 293-322.
First available in Project Euclid: 18 June 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14J45: Fano varieties
Secondary: 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
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