Intersection theory on mixed curves

Mutsuo Oka

doi:10.2996/kmj/1341401050

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Home > Journals > Kodai Math. J. > Volume 35 > Issue 2 > Article

June 2012 Intersection theory on mixed curves

Mutsuo Oka

Kodai Math. J. 35(2): 248-267 (June 2012). DOI: 10.2996/kmj/1341401050

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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 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.