Intersection theory on mixed curves

Details Intersection theory on mixed curves Intersection theory on mixed curves

2011-04-18

arxiv.org/abs/1104.3386v1

Mathematics

Algebraic Geometry

18 pages, 3 figures

Scientific paper

We consider two mixed curve $C,C'\subset {\Bbb C}^2$ which are defined by mixed functions of two variables $\bf z=(z_1,z_2)$. We have shown in \cite{MC}, that they have canonical orientations. If $C$ and $C'$ are smooth and intersect transversely at $P$, the intersection number $I_{top}(C,C';P)$ 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.

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