Multiplicity and the pull-back problem

2014/05/28 by Maciej P. Denkowski, Denkowski, Maciej P.
Mathematics · #14B05 #32A10 #32B15 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #math.AG #math.CV #msc:14B05 #msc:32A10 #msc:32B15

paper · pdf · doi:10.48550/arxiv.1405.7172

Misprints corrected

arxiv created 2014/06/18 · arxiv updated 2014/06/19

Abstract

We discuss a formula of S. Spodzieja and generalize it for the isolated improper Achilles-Tworzewski-Winiarski intersection index. As an application we give a simple proof of a result of P. Ebenfelt and L. Rothschild: if F\colon (ℂ^m,0)→ (ℂ^m,0) is a finite holomorphic map, W a germ of a complex variety at zero such that F^-1(W) is a smooth germ and the Jacobian of F does not vanish identically on it, then W is smooth too.

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