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Relative enumerative invariants of real nodal del Pezzo surfaces

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Abstract

The surfaces considered are real, rational and have a unique smooth real \((-2)\)-curve. Their canonical class K is strictly negative on any other irreducible curve in the surface and \(K^2>0\). For surfaces satisfying these assumptions, we suggest a certain signed count of real rational curves that belong to a given divisor class and are simply tangent to the \((-2)\)-curve at each intersection point. We prove that this count provides a number which depends neither on the point constraints nor on deformation of the surface preserving the real structure and the \((-2)\)-curve.

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Authors and Affiliations

  1. Institut de Mathématiques de Jussieu - Paris Rive Gauche, Sorbonne Université, 4 place Jussieu, 75252, Paris Cedex 5, France

    Ilia Itenberg

  2. Département de mathématiques et applications, Ecole Normale Supérieure, 45 rue d’Ulm, 75230, Paris Cedex 5, France

    Ilia Itenberg

  3. Université de Strasbourg et IRMA, 7, rue René Descartes, 67084, Strasbourg Cedex, France

    Viatcheslav Kharlamov

  4. School of Mathematical Sciences, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, 69978, Tel Aviv, Israel

    Eugenii Shustin

Authors
  1. Ilia Itenberg
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  2. Viatcheslav Kharlamov
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  3. Eugenii Shustin
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Correspondence to Eugenii Shustin.

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Itenberg, I., Kharlamov, V. & Shustin, E. Relative enumerative invariants of real nodal del Pezzo surfaces. Sel. Math. New Ser. 24, 2927–2990 (2018). https://doi.org/10.1007/s00029-018-0418-y

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  • DOI: https://doi.org/10.1007/s00029-018-0418-y

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