A complete characterization of A_0-sufficiency of plane-to-plane jets of rank 1

Olav Skutlaberg

Journal of Singularities
volume 3 (2011), 89-112

Received: 22 June 2010. Received in revised form: 5 May 2011.

DOI: 10.5427/jsing.2011.3f

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Sufficient conditions for A_0-sufficiency of plane-to-plane r-jets are known. These conditions are stated in the form of two Lojasiewicz inequalities which have to be satisfied. The first of these inequalities is known to be necessary for A_0-sufficiency, and in this article we prove that the second inequality is also necessary for A_0-sufficiency of all jets of rank 1. We also prove that a simpler Lojasiewicz inequality is equivalent to the second inequality for rank 1 jets.

Author(s) information:

Olav Skutlaberg
Matematisk Institutt
Universitetet i Oslo
Postboks 1053 Blindern
0316 Oslo, Norway
email: oskutlab@math.uio.no