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Equivariant Compactifications of Two-Dimensional Algebraic Groups

Part of: Diophantine equations Surfaces and higher-dimensional varieties Algebraic groups

Published online by Cambridge University Press:  27 October 2014

Ulrich Derenthal  and
Daniel Loughran
Ulrich Derenthal
Affiliation:
Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, Weifengerten 1, 30167 Hannover, Germany, (derenthal@math.uni-hannover.de; loughran@math.uni-hannover.de)
Daniel Loughran
Affiliation:
Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Leibniz Universität Hannover, Weifengerten 1, 30167 Hannover, Germany, (derenthal@math.uni-hannover.de; loughran@math.uni-hannover.de)
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Abstract

We classify generically transitive actions of semi-direct products on ℙ2. Motivated by the program to study the distribution of rational points on del Pezzo surfaces (Manin's conjecture), we determine all (possibly singular) del Pezzo surfaces that are equivariant compactifications of homogeneous spaces for semi-direct products .

Keywords

del Pezzo surfacesalgebraic groupsequivariant compactificationsManin's conjectures

MSC classification

Primary: 14L30: Group actions on varieties or schemes (quotients)
Secondary: 14J26: Rational and ruled surfaces 11D45: Counting solutions of Diophantine equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 58 , Issue 1 , February 2015 , pp. 149 - 168
Copyright
Copyright © Edinburgh Mathematical Society 2015 

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