Rokhlin’s Formula for Dividing T-Curves
نویسنده
چکیده
A nonsingular real algebraic plane projective curve is called a dividing curve or a curve of type I if its real point set divides its complex point set. Rokhlin’s formula, which holds for such curves, is an important step in order to classify nonsingular real algebraic plane projective curves. It gives prohibitions on the complex orientations of a curve of type I and also on its real scheme. The concept of type has been defined also for T-curves which are PL-curves constructed using a combinatorial method called T-construction. From the point of view of real algebraic geometry, this construction is very interesting because, under a condition of ”convexity” of the triangulation used in the T-construction, the resulting Tcurve has the isotopy type of a nonsingular real algebraic plane projective curve. In this work we prove that Rokhlin’s formula holds for dividing primitive T-curves constructed with arbitrary (not necessary convex) triangulations.
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