Log minimal model program for the moduli space of stable curves: The second flip

Abstract

We prove an existence theorem for good moduli spaces, and use it to construct the second flip in the log minimal model program for the moduli space of stable curves. In fact, our methods give a uniform, self-contained construction of the first three steps of the log minimal model program for the moduli spaces of stable pointed curves.

v2: a major revision with streamlined arguments and improved exposition. The definition of the functor at α=2/3-ε is slightly modified. 94 pages, 11 figures. Comments are welcome

References in corpus (2)

• Singularities with G_m-action and the log minimal model program for ${\bar{M}}_g$
• Log canonical models and variation of GIT for genus four canonical curves

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• Universal moduli spaces of vector bundles and the log-minimal model program on the moduli of curves