The complex separation and extensions of Rokhlin congruence for curves on surfaces
| dc.creator | Mikhalkin, G. | |
| dc.date | 1992-06-24 | |
| dc.date.accessioned | 2026-07-07T09:05:45Z | |
| dc.date.available | 2026-07-07T09:05:45Z | |
| dc.description | The 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.description | 17 pages, LaTeX | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9206009 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9206009 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149781 | |
| dc.subject | Algebraic Geometry | |
| dc.title | The complex separation and extensions of Rokhlin congruence for curves on surfaces | |
| dc.type | text |