Log canonical models for the moduli space of curves: The first divisorial contraction

By Brendan Hassett, Donghoon Hyeon. 2006

135 citations recorded by the source corpus.

In this paper, we initiate our investigation of log canonical models for (M g , αδ) as we decrease α from 1 to 0. We prove that for the first critical value α = 9/11, the log canonical model is isomorphic to the moduli space of pseudostable curves, which have nodes and cusps as singularities. We also show that α = 7/10 is the next critical value, i.e., the log canonical model stays the same in the interval (7/10,9/11]. In the appendix, we develop a theory of log canonical models of stacks that explains how these can be expressed in terms of the coarse moduli space.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/39c13e672973e3dd26eb9f429e8863b9fa535393

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Alternate Compactifications of Moduli Spaces of Curves (2010, unknown): “11 ([HH09] and [HH08]).”
Modular compactifications of the space of pointed elliptic curves II (2010, methodology): “In this notation, results of Hassett and Hyeon [HH09, HH] give Theorem (Hassett-Hyeon) . where M is the moduli space of pseudostable curves (in which elliptic tails are replaced by cusps) and M qs g is the moduli space of quasistable curves (in which elliptic tails and bridges are replaced by cusps…”
Log minimal model program for the moduli space of stable curves: The first flip (2008, background): “Our previous paper [HH09] describes Mg(α) explicitly for large values of α.”
Koszul modules and Green’s conjecture (2018, unknown): “The construction and geometry ofM ps g is described in [27] and [19].”