Relative enumerative invariants of real nodal del Pezzo surfaces

• Ilia Itenberg ^[1] ; Viatcheslav Kharlamov ^[2] ; Eugenii Shustin ^[3]
  1. [1] Institut de Mathématiques de Jussieu

     Institut de Mathématiques de Jussieu

     París, Francia

     
  2. [2] University of Strasbourg

     University of Strasbourg

     Arrondissement de Strasbourg-Ville, Francia

     
  3. [3] Tel Aviv University

     Tel Aviv University

     Israel

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 4, 2018, págs. 2927-2990
• Idioma: inglés
• DOI: 10.1007/s00029-018-0418-y
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• Resumen

  • 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 K2 > 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.