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Singular del Pezzo surfaces that are equivariant compactifications

Journal of Mathematical Sciences volume 171, pages 714–724 (2010)Cite this article

We determine which singular del Pezzo surfaces are equivariant compactifications of \( \mathbb{G}_{\text{a}}^2 \), to assist with proofs of Manin’s conjecture for such surfaces. Additionally, we give an example of a singular quartic del Pezzo surface that is an equivariant compactification of \( {\mathbb{G}_{\text{a}}} \) ⋊ \( {\mathbb{G}_{\text{m}}} \). Bibliography: 32 titles.

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Authors and Affiliations

  1. Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany

    U. Derenthal

  2. Department of Mathematics, University of Bristol, Bristol, UK

    D. Loughran

Authors
  1. U. Derenthal
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  2. D. Loughran
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Correspondence to U. Derenthal.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 377, 2010, pp. 26–43.

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Derenthal, U., Loughran, D. Singular del Pezzo surfaces that are equivariant compactifications. J Math Sci 171, 714–724 (2010). https://doi.org/10.1007/s10958-010-0174-9

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Keywords

  • Pezzo Surface
  • Equivariant Compactifications