Moduli of crimping data -- Frederick van der Wyck, November 14, 2008

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A nodal curve is determined by its normalization, marked with
the points lying over its nodes.  The same holds for a curve
with ordinary cusps.  But to specify a curve with other
singularities, extra "crimping data" are necessary beyond the
isomorphism types of the singularities.  We explain this
phenomenon and relate it to the local deformation theory of
singular curves in characteristic zero and in positive
characteristic.  Then we construct a global moduli space of
crimping data and give a structure theorem for it.  We show how
to compactify the space in certain cases and see what this
tells us about the global moduli theory of singular curves.