On a basis for $H_ 2(\overline M_ g)$
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- by Gabino González Díez PDF
- Proc. Amer. Math. Soc. 113 (1991), 335-344 Request permission
Abstract:
In the moduli space ${\overline {\mathbf {M}} _{\mathbf {g}}}$ of stable curves (Riemann surfaces with nodes) we construct a basis for the second homology group, which is dual to the standard basis for the second cohomology group. The elements of our basis are algebraic curves.References
- W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 4, Springer-Verlag, Berlin, 1984. MR 749574, DOI 10.1007/978-3-642-96754-2
- Walter L. Baily Jr., The decomposition theorem for $V$-manifolds, Amer. J. Math. 78 (1956), 862–888. MR 100103, DOI 10.2307/2372472
- W. L. Baily, On the imbedding of $V$-manifolds in projective space, Amer. J. Math. 79 (1957), 403–430. MR 100104, DOI 10.2307/2372689
- Lipman Bers, Spaces of degenerating Riemann surfaces, Discontinuous groups and Riemann surfaces (Proc. Conf., Univ. Maryland, College Park, Md., 1973) Ann. of Math. Studies, No. 79, Princeton Univ. Press, Princeton, N.J., 1974, pp. 43–55. MR 0361051
- Hershel M. Farkas and Irwin Kra, Riemann surfaces, Graduate Texts in Mathematics, vol. 71, Springer-Verlag, New York-Berlin, 1980. MR 583745, DOI 10.1007/978-1-4684-9930-8
- E. Freitag, Siegelsche Modulfunktionen, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 254, Springer-Verlag, Berlin, 1983 (German). MR 871067, DOI 10.1007/978-3-642-68649-8
- Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York, 1978. MR 507725 J. Harris, Recent work on ${{\mathbf {M}}_{\mathbf {g}}}$, Proc. Internat. Congress of Math., Warszawa, 1983.
- Joe Harris and David Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67 (1982), no. 1, 23–88. With an appendix by William Fulton. MR 664324, DOI 10.1007/BF01393371
- Subhashis Nag, The complex analytic theory of Teichmüller spaces, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons, Inc., New York, 1988. A Wiley-Interscience Publication. MR 927291
- I. Satake, On a generalization of the notion of manifold, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 359–363. MR 79769, DOI 10.1073/pnas.42.6.359
- Scott Wolpert, On the homology of the moduli space of stable curves, Ann. of Math. (2) 118 (1983), no. 3, 491–523. MR 727702, DOI 10.2307/2006980
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 113 (1991), 335-344
- MSC: Primary 14H15; Secondary 32G15
- DOI: https://doi.org/10.1090/S0002-9939-1991-1072086-X
- MathSciNet review: 1072086