Ambient Surfaces and T-Fillings of T-Curves

Details Ambient Surfaces and T-Fillings of T-Curves Ambient Surfaces and T-Fillings of T-Curves

1999-01-06

arxiv.org/abs/math/9901018v1

Mathematics

Algebraic Geometry

LaTeX2e, 33 pages, 18 figures

Scientific paper

T-curves are piecewise linear curves which have been used with success since the beginning of the 1990's to construct new real algebraic curves with prescribed topology mainly on the real projective plane. In fact T-curves can be used on any real projective toric surface. We generalize here the construction of the latter by departing from non-convex polygons and we get a class of surfaces, the ambient surfaces, that we characterize topologically and on which T-curves are also well defined. Associated to each T-curve we construct a surface, the T-filling, which is topologically the analog of the quotient of the complexification of a real algebraic curve by the complex conjugation. We use then the T-filling to prove a theorem for T-curves on arbitrary ambient surfaces which is the analog of a theorem of Harnack for algebraic curves, and to define the orientability and orientation of a T-curve, the same way it is defined in the real algebraic setting.

Affiliated with

Also associated with

No associations

Rating

Ambient Surfaces and T-Fillings of T-Curves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Ambient Surfaces and T-Fillings of T-Curves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Ambient Surfaces and T-Fillings of T-Curves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-201543