Regular del Pezzo surfaces with irregularity

Maddock, Zachary

doi:10.1090/jag/650

Author: Zachary Maddock
Journal: J. Algebraic Geom. 25 (2016), 401-429
DOI: https://doi.org/10.1090/jag/650
Published electronically: February 24, 2016
MathSciNet review: 3493588
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Abstract | References | Additional Information

Abstract:

We construct the first examples of regular del Pezzo surfaces $X$ for which ℎ¹(𝒪

_{𝒳})>0.

We also find a restriction on the integer pairs that are possible as the anti-canonical degree $K_X^2$ and irregularity $h^1(\mathcal {O}_X)$ of such a surface. Our method of proof is by generalizing results of Ekedahl on foliations to the setting of regular varieties.

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Additional Information

Zachary Maddock
Email: maddockz@gmail.com

Received by editor(s): November 1, 2012
Received by editor(s) in revised form: July 20, 2013, and August 8, 2013
Published electronically: February 24, 2016
Additional Notes: This work was supported by the NSF through a Graduate Research Fellowship
Article copyright: © Copyright 2016 University Press, Inc.