2010/06/06 by Donghoon Hyeon, Hyeon, Donghoon
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.1006.1094
13 pages, 2 figures
arxiv created 2011/03/29 · arxiv updated 2011/03/30
Hassett and Keel predicted that there is a descending sequence of critical α values where the log canonical model for the moduli space of stable curves with respect to αδ changes. We derive a conjectural formula for the critical values in two different ways, by working out the intersection theory of the moduli space of hyperelliptic curves and by computing the GIT stability of certain curves with tails and bridges. The results give a rough outline of how the log minimal model program would proceed, telling us when the log canonical model changes and which curves are to be discarded and acquired at the critical steps.