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manin's conjectures

Proceedings of the Edinburgh Mathematical Society (1)

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Equivariant Compactifications of Two-Dimensional Algebraic Groups
Part of
Ulrich Derenthal, Daniel Loughran
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 58 / Issue 1 / February 2015

Published online by Cambridge University Press:

27 October 2014, pp. 149-168
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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 .