Toward a canonical model for the moduli space of curves
-- Brendan Hassett, December 5, 2003

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This is joint with D. Hyeon.  Consider the moduli space of
stable curves as a log-variety, with boundary delta
corresponding to the nodal curves.  We seek to describe its log
canonical model with respect to K + A delta.  When A = 1, we
recover the moduli space of stable curves; for A = 0, this
would be the canonical model of the moduli space, which is
expected to exist for g > 23 after work of Eisenbud, Harris, and
Mumford.  For intermediate values of A, the log canonical model
can be constructed with Geometric Invariant Theory.  As A
decreases, the log canonical model parametrizes curves with
increasingly complicated singularities: cusps, tacnodes, and
worse.