Let C [subset] [P.sup.2] be a smooth plane curve
of degree d (d [greater than or equal to] 4) and C(C) the function field of C.
On the other hand, the profiles of plane curves
or intersurface attracted more and more attention.
In this short note we want to compare two approaches to compute the Euler characteristic of the Milnor fibre of a plane curve
(iii) If q = 0, then c [is less than or equal to] 5 and c = 5 precisely when C is a plane curve
of degree 9.
In this article, we continue to study Zariski pairs for reducible plane curves
based on the idea used in .
Since C is smooth, we see that C is isomorphic to a plane curve
of degree [greater than or equal to] 8, contradicting the assumption g [less than or equal to] 3.
Theorem 8 Let [x(s), y(s)] be a regular parametric plane curve
of class [C.sub.3], and P be a point which is not a point of [x(s), y(s)], and the tangents of [x(s), y(s)] do not pass through P.
Other topics include conjugate vectors of immersed manifolds, Thom polynomials and Schur functions, obstructions on fundamental groups of plane curve
complements, and exotic moduli of Goursat distributions.
Fundamental groups of plane curve
complements play an important role in the study of branched coverings.
has no [g.sup.1.sub.2]) the real plane curve
obtained by this net has only points of multiplicity at most 2.
Thus, we refer to a spline plane curve
defined in this way.