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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.24 no.3 Antofagasta Dec. 2005

http://dx.doi.org/10.4067/S0716-09172005000300005 

 

Proyecciones
Vol. 24, No 3, pp. 257-276, December 2005.
Universidad Católica del Norte
Antofagasta - Chile

 

TOPOLOGICAL CLASSIFICATION OF COMPACT SURFACES WITH NODES OF GENUS 2

 

IGNACIO GARIJO

Universidad Nacional de Educación a Distancia, España


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]).

 

References

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

[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).         [ Links ]

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

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

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

[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).         [ Links ]

 

IGNACIO C. GARIJO
Departamento de Matemáticas Fundamentales
Facultad de Ciencias
Universidad Nacional de Educación a Distancia
c/ Senda del Rey, 9
28040-Madrid
España

Received : April 2005. Accepted : November 2005

 

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