# Webs of rational curves on real surfaces and a classification of real weak del Pezzo surfaces

@article{Lubbes2020WebsOR, title={Webs of rational curves on real surfaces and a classification of real weak del Pezzo surfaces}, author={Niels Lubbes}, journal={Journal of the London Mathematical Society}, year={2020}, volume={103} }

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 two classifications are related to root subsystems of E8.

## One Citation

### Surfaces that are covered by two pencils of circles

- Mathematics
- 2021

We list up to M\"obius equivalence all possible degrees and embedding dimensions of real surfaces that are covered by at least two pencils of circles, together with the number of such pencils. In…

## References

SHOWING 1-10 OF 45 REFERENCES

### Explicit Real Cubic Surfaces

- MathematicsCanadian Mathematical Bulletin
- 2008

Abstract The topological classification of smooth real cubic surfaces is recalled and compared to the classification in terms of the number of real lines and of real tritangent planes, as obtained by…

### Computing curves on real rational surfaces

- Mathematics, Computer ScienceArXiv
- 2018

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.

### Real Algebraic Surfaces

- Mathematics
- 1997

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.…

### Real Algebraic Surfaces

- Mathematics
- 1989

Results on real algebraic surfaces show linear cycles on real varieties and application to rational surfaces are similar to that on real abelian varieties.

### The Multiple Conical Surfaces

- Mathematics
- 2001

We give a classification of the surfaces that can be generated by a moving conic in more than one way. It turns out that these surfaces belong to classes which have been thoroughly studied in other…

### ALGORITHMS FOR SINGULARITIES AND REAL STRUCTURES OF WEAK DEL PEZZO SURFACES

- Mathematics
- 2014

In this paper, we consider the classification of singularities [P. Du Val, On isolated singularities of surfaces which do not affect the conditions of adjunction. I, II, III, Proc. Camb. Philos.…

### 3-Webs generated by confocal conics and circles

- Mathematics, Physics
- 2016

We consider families of confocal conics and two pencils of Apollonian circles having the same foci. We will show that these families of curves generate trivial 3-webs and find the exact formulas…

### Classification of regular three-webs formed by pencils of circles

- Mathematics
- 2007

We prove that there exist no regular three-webs except for those listed by V. Lazareva.

### Real forms of smooth del Pezzo surfaces.

- Mathematics
- 1987

Work on real forms is also classical: for cubic surfaces, beginning with Schl fli [13]; for quartic curves the best reference is Zeuthen [21] (see also [5]); while for a surface of intersection of…