Minimal degree rational curves on real surfaces

@article{Lubbes2019MinimalDR,
  title={Minimal degree rational curves on real surfaces},
  author={Niels Lubbes},
  journal={Advances in Mathematics},
  year={2019}
}
  • Niels Lubbes
  • Published 13 June 2018
  • Mathematics
  • Advances in Mathematics
We classify real families of minimal degree rational curves that cover an embedded rational surface. A corollary is that if the projective closure of a smooth surface is not biregular isomorphic to the projective closure of the unit-sphere, then the set of minimal degree rational curves that cover the surface is either empty or of dimension at most two. Moreover, if these curves are of minimal degree over the real numbers, but not over the complex numbers, then almost all the curves are smooth… Expand
1 Citations
Webs of rational curves on real surfaces and a classification of real weak del Pezzo surfaces
We classify webs of minimal degree rational curves on surfaces and give a criterion for webs being hexagonal. In addition, we classify Neron-Severi lattices of real weak del Pezzo surfaces. These twoExpand

References

SHOWING 1-10 OF 28 REFERENCES
Minimal families of curves on surfaces
  • Niels Lubbes
  • Computer Science, Mathematics
  • J. Symb. Comput.
  • 2014
TLDR
The minimal lexicographic degree for the parametrization of a surface that carries at least 2 minimal families is determined and is generalize some results of Schicho. Expand
A degree bound for families of rational curves on surfaces
  • Niels Lubbes
  • Mathematics
  • Journal of Pure and Applied Algebra
  • 2019
We give an upper bound for the degree of rational curves in a family that covers a given birational ruled surface in projective space. The upper bound is stated in terms of the degree, sectionalExpand
Families of bitangent planes of space curves and minimal non-fibration families
We define a cone curve to be a reduced sextic space curve which lies on a quadric cone and does not go through the vertex. We classify families of bitangent planes of cone curves. The methods weExpand
Real Algebraic Surfaces
The aim of these lectures is to study real algebraic surfaces with the help of the minimal model program. I mainly concentrate on those surfaces F which are rational over C. In some sense this is theExpand
Lattice polygons and families of curves on rational surfaces
First we solve the problem of finding minimal degree families on toric surfaces by reducing it to lattice geometry. Then we describe how to find minimal degree families on, more generally, rationalExpand
Complex Algebraic Surfaces
Introduction Notation Part I. The Picard Group and the Riemann-Roch Theorem: Part II. Birational Maps: Part III. Ruled Surfaces: Part IV. Rational Surfaces: Part V. Castelnuovo's Theorem andExpand
Real Algebraic Surfaces
These are the notes for my lectures at the Trento summer school held September 1997. The aim of the lectures is to provide an introduction to real algebraic surfaces using the minimal model program.Expand
Computing curves on real rational surfaces
TLDR
This work presents an algorithm for computing curves and families of curves of prescribed degree and geometric genus on real rational surfaces and shows how this algorithm can be modified for curved topographies. Expand
Rational curves on algebraic varieties
  • J. Kollár
  • Mathematics, Computer Science
  • Ergebnisse der Mathematik und ihrer Grenzgebiete
  • 1996
TLDR
It is shown here how the model derived recently in [Bouchut-Boyaval, M3AS (23) 2013] can be modified for flows on rugous topographies varying around an inclined plane. Expand
Computing basepoints of linear series in the plane
TLDR
An algorithm for detecting basepoints of linear series of curves in the plane of classical procedure of blowing up points in the planes is presented and the algorithmic version of this procedure with several applications is motivated. Expand
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