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

Abstract

We introduce and compute the class of a number of effective divisors on the moduli space of stable maps ${\bar{M}}_{0,0}(P^r,d)$, 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.

Main paper by Chen and Coskun, with a Macaulay 2 program in the appendix by Crissman to verify certain moving curves

References in corpus (5)

• Existence of minimal models for varieties of log general type
• Log minimal model program for the moduli space of stable curves: The first flip
• On Log Canonical Models of the Moduli Space of Stable Pointed Curves
• Log minimal model program for the moduli space of stable curves of genus three
• Modular compactifications of M_{1,n}