Towards Mori's program for the moduli space of stable maps

2009/05/18 by Chen, Dawei, Coskun, Izzet, Crissman, Charley
#14D22 #14E05 #14E30 #14H10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0905.2947

Abstract

We introduce and compute the class of a number of effective divisors on the moduli space of stable maps M_0,0(P^r,d), which, for small d, provide a good understanding of the extremal rays and the stable base locus decomposition for the effective cone. We also discuss various birational models that arise in Mori's program, including the Hilbert scheme, the Chow variety, the space of k-stable maps, the space of branchcurves and the space of semi-stable sheaves.

Related

• Mori's program for the moduli space of conics in Grassmannian
• The geometry of the moduli space of one-dimensional sheaves
• Integral points and effective cones of moduli spaces of stable maps
• Positive divisors on quotients of M_0,n and the Mori cone of M_g,n
• Variation of stability for moduli spaces of unordered points in the plane