Asymptotic behaviour of rational curves

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.Comment: 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, Grenobl