Rational curves on the compactified moduli space of rational curves with marked points

2012/12/29 by Shachar Carmeli, Carmeli, Shachar, Lev Radzivilovsky +1
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.1212.6642

Abstract

We investigate the possible homological classes of rational curves on the moduli space X_n=M_0,n of rational nodal curves with n marked points. In the case of X₅ and X₆ the relevant homology classes belong to certain polyhedral cones which we describe explicitly. Not all homology classes in the cone correspond to rational curves, but all classes sufficiently far from the walls of the cone do. The proof for X₅ is explicit, the proof for X₆ was carried out using computers.

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