Exemples de comptage de courbes sur les surfaces

Abstract : Let X be a surface whose Cox ring has a single relation satisfying moreover a kind of linearity property. Under a simple assumption, we show that the geometric Manin's conjectures hold for some degrees lying in the dual of the effective cone of X (in particular, for those degrees the moduli space of morphisms has the expected dimension). The result applies to a class of generalized del Pezzo surfaces which has been intensively studied in the context of the arithmetic Manin's conjecture.
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Submitted on : Tuesday, May 15, 2012 - 5:02:21 PM
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David Bourqui. Exemples de comptage de courbes sur les surfaces. Mathematische Annalen, Springer Verlag, 2013, 357 (4), pp.1291-1327. ⟨10.1007/s00208-013-0933-2⟩. ⟨hal-00697614⟩

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