Intersection theory on mixed curves

Abstract

We consider two mixed curve $C,C^{\prime }\subset {\mathbb{C}}^2$ which are defined by mixed functions of two variables $\mathbf{z}=({\mathbf{z}}_1,{\mathbf{z}}_2)$. We have shown in \cite{MC}, that they have canonical orientations. If $C$ and $C^{\prime }$ are smooth and intersect transversely at $P$, the intersection number $I_{top}(C,C^{\prime };P)$ is topologically defined. We will generalize this definition to the case when the intersection is not necessarily transversal or either $C$ or $C^{\prime }$ may be singular at $P$ using the defining mixed polynomials.

18 pages, 3 figures

References in corpus (1)

• On mixed projective curves