Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On a basis for $ H\sb 2(\overline M\sb g)$

Author: Gabino González Díez
Journal: Proc. Amer. Math. Soc. 113 (1991), 335-344
MSC: Primary 14H15; Secondary 32G15
MathSciNet review: 1072086
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [BPV] W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Springer-Verlag, New York, 1984. MR 749574 (86c:32026)
  • [Ba1] W. L. Baily, The decomposition theorem for $ V$-manifolds, Amer. J. Math. 78 (1956), 862-888. MR 0100103 (20:6537)
  • [Ba2] -, On the imbedding of $ V$-manifolds in projective space, Amer. J. Math. 79 (1957), 403-430. MR 0100104 (20:6538)
  • [Be] L. Bers, Spaces of degenerating Riemann surfaces, Ann. of Math. Studies, vol. 79, Princeton Univ. Press, Princeton, NJ, 1974. MR 0361051 (50:13497)
  • [FK] H. Farkas and I. Kra, Riemann surfaces Springer-Verlag, New York, 1980. MR 583745 (82c:30067)
  • [Fr] E. Freitag, Siegelsche Modulfunktionen, Springer-Verlag, New York, 1983. MR 871067 (88b:11027)
  • [GH] P. Griffiths and Harris, Principles of algebraic geometry, Wiley, New York, 1978. MR 507725 (80b:14001)
  • [H] J. Harris, Recent work on $ {{\mathbf{M}}_{\mathbf{g}}}$, Proc. Internat. Congress of Math., Warszawa, 1983.
  • [HM] J. Harris and D. Mumford, On the Kodaira dimension of the moduli space of curves, Invent. Math. 67, (1982), 23-86. MR 664324 (83i:14018)
  • [Na] S. Nag, The complex analytic theory of Teichmüller spaces, Wiley, New York, 1988. MR 927291 (89f:32040)
  • [Sa] I. Satake, On a generalization of the notion of manifold, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 359-363. MR 0079769 (18:144a)
  • [Wo] S. Wolpert, On the homology of the moduli space of stable curves, Ann. of Math. (2) 118 (1983), 491-523. MR 727702 (86h:32036)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14H15, 32G15

Retrieve articles in all journals with MSC: 14H15, 32G15

Additional Information

Article copyright: © Copyright 1991 American Mathematical Society

American Mathematical Society