Equivariant Compactifications of Two-Dimensional Algebraic Groups

Ulrich Derenthal, Daniel Loughran

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    Abstract

    We classify generically transitive actions of semi-direct products Ga ⋊ Gm 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 Ga ⋊ Gm.

    Original languageEnglish
    Pages (from-to)149-168
    Number of pages20
    JournalProceedings of the Edinburgh Mathematical Society
    Volume58
    Issue number1
    DOIs
    Publication statusPublished - 16 Apr 2014

    Keywords

    • algebraic groups
    • del Pezzo surfaces
    • equivariant compactifications
    • Manin's conjectures

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