Second flip in the Hassett-Keel program: A local description

Jarod Alper, Maksym Fedorchuk, David Ishii Smyth, Frederick Van Der Wyck

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    12 Citations (Scopus)

    Abstract

    This is the first of three papers in which we give a moduli interpretation of the second flip in the log minimal model program for , replacing the locus of curves with a genus Weierstrass tail by a locus of curves with a ramphoid cusp. In this paper, for , we introduce new -stability conditions for curves and prove that they are deformation open. This yields algebraic stacks related by open immersions . We prove that around a curve corresponding to a closed point in , these open immersions are locally modeled by variation of geometric invariant theory for the action of on the first-order deformation space of C.

    Original languageEnglish
    Pages (from-to)1547-1583
    Number of pages37
    JournalCompositio Mathematica
    Volume153
    Issue number8
    DOIs
    Publication statusPublished - 1 Aug 2017

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