Asymptotic behaviour of rational curves

2011/07/19 by David Bourqui, Bourqui, David · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Geometric Analysis and Curvature Flows #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1107.3824

This is a revised and slightly expanded version of notes for a course delivered during the summer school on rational curves held in June 2010 at Institut Fourier, Grenoble

arxiv created 2011/07/19 · openalex publication_date 2011/07/19 · arxiv updated 2011/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the asympotic behaviour of the moduli space of morphisms from the rational curve to a given variety when the degree becomes large. One of the crucial tools is the homogeneous coordinate ring of the variey. First we explain in details what happens in the toric case. Then we examine the general case.

Citations

• An overview of Manin's conjecture for del Pezzo surfaces
• Rational points on some Fano cubic bundles
• Fonctions L d'Artin et nombre de Tamagawa motiviques
• Rational points of bounded height on Fano varieties
• Hauteurs et mesures de Tamagawa sur les variétés de Fano
• Points de hauteur bornee sur les varietes de drapeaux en caracteristique finie

Cited by

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

Related

• Asymptotic directions in the moduli space of curves
• Towards large genus asymtotics of intersection numbers on moduli spaces of curves
• Rational curves on blowing-ups of projective spaces
• Rational points, genus and asymptotic behaviour in reduced algebraic curves over finite fields
• Dimension counts for singular rational curves via semigroups