Topological classification of compact surfaces with nodes of genus 2

Authors

  • Ignacio C. Garijo Universidad Nacional de Educación a Distancia.

DOI:

https://doi.org/10.4067/S0716-09172005000300005

Abstract

We associate to each Riemann or Klein surface with nodes a graph that classifies it up homeomorphism. We obtain that, for surfaces of genus two, there are 7 topological types of stable Riemann surfaces, 33 topological types of stable Klein surfaces and 35 topological types of symmetric stable Riemann surfaces (this last type of surfaces corresponds to the new surfaces appearing in the compactification of the Moduli space of real algebraic curves, see [Se] and [Si]).

Author Biography

Ignacio C. Garijo, Universidad Nacional de Educación a Distancia.

Departamento de Matemáticas, Fundamentales Facultad de Ciencias.

References

[A-G] N. L. Alling, N. Greenleaf, Foundations of the Theory of Klein Surfaces. Lecture Notes in Math., 219, Springer, (1971).

[D-M] P. Deligne, D. Mumford, The irreducibility of the space of curves of given genus. Inst. Hautes Etudes Sci. Publ. Math., 36, pp. 75-109, (1969).

[G1] I. Garijo, Superficies de Riemann y Klein con nodos. Ph. D. Thesis, U. N. E. D., (2000).

[G2] I. Garijo, The double covers of Klein surfaces with nodes. ArXiv: math.CV/0505182, vol. 1 10 May (2005).

[K] M. Kontsevich, Intersection theory on the moduli space of curves and the matrix Airy function. Communications in Mathematical Physics, 147, pp. 1-23, (1992).

[L-Z] S. K. Lando, A. K. Zvonkin, Graphs on surfaces and their applications. Encyclopedia of Mathematical Sciences, Vol. 141, Springer, Berlin, (2004).

[Se] M. Seppäla, Moduli space of stable real algebraic curves. Ann. Scient. Ec. Norm. Sup., 4e série, 24, pp. 519-544, (1991).

[Si] R. Silhol, Compactification of moduli spaces in real algebraic geometry. Invent. Math., 107, pp. 151-202, (1992).

[Z] D. Zvonkine, Strebel differentials on stable curves and Kontsevich’s proof of Witten’s conjecture. Preprint, arXiv: math. AG/0209071, Vol. 2 7 Jan (2004).

Published

2017-04-20

How to Cite

[1]
I. C. Garijo, “Topological classification of compact surfaces with nodes of genus 2”, Proyecciones (Antofagasta, On line), vol. 24, no. 3, pp. 257-276, Apr. 2017.

Issue

Section

Artículos