The polars as adjoint curves.
The polars as adjoint curves.
As everybody knows, if C is a plane curve, 0 is a point of C of multiplicity \(\mu\), and C' is a polar curve of C, then C' passes through 0 with multiplicity \(\mu\) '\(\geq \mu -1\). In the present paper it is pointed out that, whatever the characteristic of the base field, if C is reduced it is not true, in general, that a polar curve C' passes with multiplicity at least r-1 through every singular point of C of multiplicity r, infinitely near to 0. Sufficient conditions for this to happen, at least for polars of points different from 0, are given in characteristic zero.
plane curve, multiplicity, Arithmetic ground fields for curves, Singularities of curves, local rings, polar curve
plane curve, multiplicity, Arithmetic ground fields for curves, Singularities of curves, local rings, polar curve
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