English

Exemples de comptage de courbes sur les surfaces

Algebraic Geometry 2012-05-17 v1 Number Theory

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.

Keywords

Cite

@article{arxiv.1205.3573,
  title  = {Exemples de comptage de courbes sur les surfaces},
  author = {David Bourqui},
  journal= {arXiv preprint arXiv:1205.3573},
  year   = {2012}
}
R2 v1 2026-06-21T21:04:49.948Z