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Singular del Pezzo surfaces that are equivariant compactifications

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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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