Arc lifting for the Nash manifold

Details Arc lifting for the Nash manifold Arc lifting for the Nash manifold

2011-03-29

arxiv.org/abs/1103.5723v4

Mathematics

Complex Variables

Scientific paper

Let M be a singular normal irreducible complex manifold of dimension n. Let f:U-> M be the smooth Nash manifold. Theorem 1. Let g:R->M be an analytic map from a connected Riemann surface whose image contains a non singular point of M. Then there is a unique g':R->U such that g=fg'. Theorem 2. Let V be an irreducible singular submanifold containing a non singular point of M. Then V has a proper transform in the Nash manifold U if and only if the union of the stable locus of proper transforms of V in finite sequences of Nash blowups of M is proper over V.

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