BOSÁKOVÁ Adriana

Contribution of a tangent of multiplicity one to the intersection multiplicity of two plane curves

Intersection multiplicity of two plane curves F and G at some point P has a well-known property of I ≥ mn, where m and n are the multiplicities of the point P on the curves F and G respectively. To each common tangent of F and G at P can be assigned a nonnegative integer, a number equal to its contribution to the intersection multiplicity. This can be done via local investigation methods. The sum of these contribution numbers of all common tangents is equal to the remainder R = I - mn, We investigate the values of this contribution number for common tangents of the multiplicity 1.