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arXiv · 1205.3573

Exemples de comptage de courbes sur les surfaces

David Bourqui
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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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David Bourqui. 2012-05-16. Exemples de comptage de courbes sur les surfaces. https://arxiv.org/abs/1205.3573

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