The complex separation and extensions of Rokhlin congruence for curves on surfaces

dc.creatorMikhalkin, G.
dc.date1992-06-24
dc.date.accessioned2026-07-07T09:05:45Z
dc.date.available2026-07-07T09:05:45Z
dc.descriptionThe subject of this paper is the problem of arrangement of real algebraic curves on real algebraic surfaces. In this paper we extend Rokhlin, Kharlamov-Gudkov-Krakhnov and Kharlamov-Marin congruences for curves on surfaces and give some applications of this extension. For some pairs consisting of a surface and a curve on this surface (in particular for M-pairs) we introduce a new structure --- the complex separation that is separation of the complement of curve into two surfaces. In accordance with Rokhlin terminology the complex separation is a complex topological characteristic of real algebraic varieties. The complex separation is similar to complex orientations introduced by O.Ya.Viro (to the absolute complex orientation in the case when a curve is empty and to the relative complex orientation otherwise). In some cases we calculate the complex separation of a surface (for example in the case when surface is the double branched covering of another surface along a curve). With the help of these calculations applications of the extension of Rokhlin congruence gives some new restrictions for complex orientations of curves on a hyperboloid.
dc.description17 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/alg-geom/9206009
dc.identifierhttp://arxiv.org/abs/alg-geom/9206009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/149781
dc.subjectAlgebraic Geometry
dc.titleThe complex separation and extensions of Rokhlin congruence for curves on surfaces
dc.typetext

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