Exemples de comptage de courbes sur les surfaces

2012/05/16 by Bourqui, David · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1205.3573

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.

Cited by

• The spaces of rational curves on del Pezzo surfaces via conic bundles

Related

• An overview of Manin's conjecture for del Pezzo surfaces
• The Manin conjecture in dimension 2
• Manin's conjecture for quintic del Pezzo surfaces with a conic bundle structure
• Manin's conjecture for a quintic del Pezzo surface with A₂ singularity
• Manin's conjecture for a quartic del Pezzo surface with A₄ singularity