Intersection theory on mixed curves

Abstract

We consider two mixed curves C, C′ $\subset$ C2 which are defined by mixed functions of two variables z = (z1, z2). We have shown in [4], that they have canonical orientations. If C and C′ are smooth and intersect transversely at P, the intersection number Itop(C, C′; P) is topologically defined. We will generalize this definition to the case when the intersection is not necessarily transversal or either C or C′ may be singular at P using the defining mixed polynomials.