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.
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}
}