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Polar invariants of plane curve singularities: intersection theoretical approach. (English) Zbl 1202.14026

The polar invariants (also called polar quotients) of isolated hypersurface singularities are, by definition, the contact orders between the hypersurface and the branches of its generic polar curve. For this type of hypersurfaces, its Teissier collection \(\{(q, m_q)\}\), \(q\) being the polar invariants and \(m_q\) its multiplicities, constitutes an analytic invariant.
In this paper, the authors provide an overview of a number of recent results on the polar invariants of plane curve singularities that complete the well-known classical results on this subject. The authors collect their own results and others with Garcia-Barroso, being the most interesting facts the use of Newton diagrams and some applications to pencils of plane curve singularities.

MSC:

14H20 Singularities of curves, local rings
32S55 Milnor fibration; relations with knot theory
14H50 Plane and space curves
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