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On complete curves in moduli space I

Published online by Cambridge University Press:  24 October 2008

Gabino González Díez  and
William J. Harvey
Gabino González Díez
Affiliation:
Departamento de Matemáticas, Universidad Autónoma de Madrid, Spain
William J. Harvey
Affiliation:
Department of Mathematics, King's College London
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Extract

Let g denote the moduli space of compact Riemann surfaces of genus g > 3. It is known that g is a non-complete quasi-projective variety that contains many complete curves. This is because the Satake compactification g of g is projective and the boundary \ has co-dimension 2; thus by intersecting with hypersurfaces in sufficiently general position one obtains a complete curve in g passing through any given set of points [8].

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 3 , November 1991 , pp. 461 - 466
Copyright
Copyright © Cambridge Philosophical Society 1991

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References

REFERENCES

[1]Atiyah, M. F.. The signature of fiber-bundles. In Global Analysis (University of Tokyo Press, 1969), pp. 73–84.Google Scholar
[2]Bers, L.. Uniformization, moduli, and Kleinian groups. J. London Math. Soc. 4 (1972), 257–300.CrossRefGoogle Scholar
[3]Diaz, S.. A bound on the dimension of complete subvarieties of g. Duke Math. J. 51 (1984), 405–408.CrossRefGoogle Scholar
[4]Griffiths, P. and Harris, J.. Principles of Algebraic Geometry (Wiley & Sons, 1978).Google Scholar
[5]Grauert, H. and Remmert, R.. Coherent Analytic Sheaves (Springer-Verlag, 1984).CrossRefGoogle Scholar
[6]Gilman, J.. On the moduli of compact Riemann surfaces with a finite number of punctures. In Discontinuous Groups and Riemann Surfaces, Ann. of Math. Studies no. 79 (Princeton University Press, 1974), pp. 181–205.CrossRefGoogle Scholar
[7]Gonzalez-Diez, G.. Loci of curves which are prime Galois coverings of P1. Proc. London Math. Soc. (3) 60 (1991), 469–489.CrossRefGoogle Scholar
[8]Harris, J.. Recent work on g. In Proceedings of International Congress of Mathematicians, Warsaw (PWN-Polish Scientific Publishers, 1983), pp. 719–726.Google Scholar
[9]Harvey, W. J.. Cyclic groups of automorphisms of a compact Riemann surface. Quart. J. Math. Oxford Ser. (2) 17 (1966), 86–97.CrossRefGoogle Scholar
[10]Harvey, W. J.. On branch loci in Teichmüller space. Trans. Amer. Math. Soc. 153 (1971), 387–399.Google Scholar
[11]Igusa, J.. Arithmetic variety of moduli for genus two. Ann. of Math. 72 (1960), 612–649.CrossRefGoogle Scholar
[12]Jones, G. A. and Singeeman, D.. Complex Functions (Cambridge University Press, 1987).CrossRefGoogle Scholar
[13]Kas, A.. On deformations of a certain type of irregular algebraic surfaces. Amer. J. Math. 90 (1968), 789–804.CrossRefGoogle Scholar
[14]Kodaira, K.. A certain type of irregular algebraic surface. J. Analyse Math. 19 (1967), 207–215.CrossRefGoogle Scholar
[15]Maclachlan, C.. and Harvey, W. J.. On mapping class groups and Teichmüller spaces. Proc. London Math. Soc. (3) 30 (1975), 496–512.CrossRefGoogle Scholar
[16]Miller, E. Y.. The homology of the mapping class group. J. Differential Geom. 24 (1986), 1–16.CrossRefGoogle Scholar
[17]Morita, S.. Characteristic classes of surface bundles I. Bull. Amer. Math. Soc. 11 (1984), 386–389.CrossRefGoogle Scholar
[18]Nag, S.. The Complex Analytic Theory of Teichmüller spaces (Wiley & Sons, 1988).Google Scholar
[19]Rauch, H. E.. A transcendental view of the space of algebraic Riemann surfaces. Bull. Amer. Math. Soc. 71 (1965), 1–39.CrossRefGoogle Scholar
[20]Riera, G.. Semi-direct products of Fuchsian groups and uniformization. Duke Math. J. 44 (1977), 291–304.CrossRefGoogle Scholar
[21]Shabat, G. B.. Local construction of complex algebraic surfaces with respect to the universal covering. Functional Anal. Appl. 17 (1983), 157–159.CrossRefGoogle Scholar