Intersection-theoretical computations on v e r l i n e M g

Carel Faber

Banach Center Publications (1996)

  • Volume: 36, Issue: 1, page 71-81
  • ISSN: 0137-6934

Abstract

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In this paper we explore several concrete problems, all more or less related to the intersection theory of the moduli space of (stable) curves, introduced by Mumford [Mu 1].

How to cite

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Faber, Carel. "Intersection-theoretical computations on ${verline M}_{g}$." Banach Center Publications 36.1 (1996): 71-81. <http://eudml.org/doc/208584>.

@article{Faber1996,
abstract = {In this paper we explore several concrete problems, all more or less related to the intersection theory of the moduli space of (stable) curves, introduced by Mumford [Mu 1].},
author = {Faber, Carel},
journal = {Banach Center Publications},
keywords = {intersection theory of the moduli space of curves; ample divisors; curves of low genus; Chow ring; Witten conjecture; Schottky locus},
language = {eng},
number = {1},
pages = {71-81},
title = {Intersection-theoretical computations on $\{verline M\}_\{g\}$},
url = {http://eudml.org/doc/208584},
volume = {36},
year = {1996},
}

TY - JOUR
AU - Faber, Carel
TI - Intersection-theoretical computations on ${verline M}_{g}$
JO - Banach Center Publications
PY - 1996
VL - 36
IS - 1
SP - 71
EP - 81
AB - In this paper we explore several concrete problems, all more or less related to the intersection theory of the moduli space of (stable) curves, introduced by Mumford [Mu 1].
LA - eng
KW - intersection theory of the moduli space of curves; ample divisors; curves of low genus; Chow ring; Witten conjecture; Schottky locus
UR - http://eudml.org/doc/208584
ER -

References

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  1. [A-C] E. Arbarello and M. Cornalba, The Picard groups of the moduli spaces of curves, Topology 26 (1987), 153-171. Zbl0625.14014
  2. [BCOV] M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes, Comm. Math. Phys. 165 (1994), 311-428. Zbl0815.53082
  3. [C-H] M. Cornalba and J. Harris, Divisor classes associated to families of stable varieties, with applications to the moduli space of curves, Ann. Scient. École Norm. Sup. (4) 21 (1988), 455-475. Zbl0674.14006
  4. [Fa 1] C. Faber, Chow rings of moduli spaces of curves I: The Chow ring of ο v e r l i n e M 3 , Ann. of Math. 132 (1990), 331-419. Zbl0721.14013
  5. [Fa 2] C. Faber, Chow rings of moduli spaces of curves II: Some results on the Chow ring of ο v e r l i n e M 4 , Ann. of Math. 132 (1990), 421-449. Zbl0735.14021
  6. [Fa 3] C. Faber, Some results on the codimension-two Chow group of the moduli space of curves, in: Algebraic Curves and Projective Geometry (eds. E. Ballico and C. Ciliberto), Lecture Notes in Math. 1389, Springer, Berlin, 1988, 66-75. 
  7. [Ha] R. Hartshorne, Ample Subvarieties of Algebraic Varieties, Lecture Notes in Math. 156, Springer, Berlin, 1970. Zbl0208.48901
  8. [Hi 1] F. Hirzebruch, Automorphe Formen und der Satz von Riemann-Roch, in: Symposium Internacional de Topologí a Algebraica (México 1956), Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, 129-144; or: Gesammelte Abhandlungen, Band I, Springer, Berlin, 1987, 345-360. 
  9. [Hi 2] F. Hirzebruch, Characteristic numbers of homogeneous domains, in: Seminars on analytic functions, vol. II, IAS, Princeton 1957, 92-104; or: Gesammelte Abhandlungen, Band I, Springer, Berlin, 1987, 361-366. 
  10. [Ko] M. Kontsevich, Intersection Theory on the Moduli Space of Curves and the Matrix Airy Function, Comm. Math. Phys. 147 (1992), 1-23. Zbl0756.35081
  11. [Liu] Qing Liu, Courbes stables de genre 2 et leur schéma de modules, Math. Ann. 295 (1993), 201-222. 
  12. [Mu 1] D. Mumford, Towards an enumerative geometry of the moduli space of curves, in: Arithmetic and Geometry II (eds. M. Artin and J. Tate), Progr. Math. 36 (1983), Birkhäuser, 271-328. Zbl0554.14008
  13. [Mu 2] D. Mumford, On the Kodaira Dimension of the Siegel Modular Variety, in: Algebraic Geometry-Open Problems (eds. C. Ciliberto, F. Ghione and F. Orecchia), Lecture Notes in Math. 997, Springer, Berlin, 1983, 348-375. 
  14. [Wi] E. Witten, Two dimensional gravity and intersection theory on moduli space, in: Surveys in Differential Geometry (Cambridge, MA, 1990), Lehigh Univ., Bethlehem, PA, 1991, 243-310. 

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