Divisor classes associated to families of stable varieties, with applications to the moduli space of curves

Maurizio Cornalba; Joe Harris

Annales scientifiques de l'École Normale Supérieure (1988)

  • Volume: 21, Issue: 3, page 455-475
  • ISSN: 0012-9593

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Cornalba, Maurizio, and Harris, Joe. "Divisor classes associated to families of stable varieties, with applications to the moduli space of curves." Annales scientifiques de l'École Normale Supérieure 21.3 (1988): 455-475. <http://eudml.org/doc/82233>.

@article{Cornalba1988,
author = {Cornalba, Maurizio, Harris, Joe},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {Hodge class; divisor class; effective Weil divisors; effective Cartier divisors; moduli space of stable genus g curves; boundary class},
language = {eng},
number = {3},
pages = {455-475},
publisher = {Elsevier},
title = {Divisor classes associated to families of stable varieties, with applications to the moduli space of curves},
url = {http://eudml.org/doc/82233},
volume = {21},
year = {1988},
}

TY - JOUR
AU - Cornalba, Maurizio
AU - Harris, Joe
TI - Divisor classes associated to families of stable varieties, with applications to the moduli space of curves
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1988
PB - Elsevier
VL - 21
IS - 3
SP - 455
EP - 475
LA - eng
KW - Hodge class; divisor class; effective Weil divisors; effective Cartier divisors; moduli space of stable genus g curves; boundary class
UR - http://eudml.org/doc/82233
ER -

References

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  1. [1] S. Ju. ARAKELOV, Families of Algebraic Curves with Fixed Degeneracies (Math. U.S.S.R. Izvestija, Vol. 35, 1971, pp. 1277-1301). Zbl0248.14004MR48 #298
  2. [2] E. ARBARELLO and M. CORNALBA, The Picard Groups of the Moduli Spaces of Curves (Topology, Vol. 26, 1987, pp. 153-171). Zbl0625.14014MR88e:14032
  3. [3] A. BEAUVILLE, Prym Varieties and the Schottky Problem (Invent. Math., Vol. 41, 1977, pp. 149-196). Zbl0333.14013MR58 #27995
  4. [4] W. FULTON, Intersection Theory, Springer Verlag, Berlin, 1984. Zbl0541.14005MR85k:14004
  5. [5] J. HARER, The Second Homology Group of the Mapping Class Group of an Orientable Surface (Invent. Math., Vol. 72, 1983, pp. 221-239). Zbl0533.57003MR84g:57006
  6. [6] J. HARER, The Cohomology of the Moduli Space of Curves, in Theory of Moduli, E. SERNESI, Ed. (Lecture Notes in Mathematics, n° 1337, Springer-Verlag, Berlin, 1988, pp. 138-221). Zbl0707.14020MR90a:32026
  7. [7] J. HARRIS, Families of Smooth Curves (Duke Math. J., Vol. 51, 1984, pp. 409-419). Zbl0548.14009MR85j:14043
  8. [8] J. HARRIS and D. MUMFORD, On the Kodaira Dimension of the Moduli Space of Curves (Invent. Math., Vol. 67, 1982, pp. 23-86). Zbl0506.14016MR83i:14018
  9. [9] R. HARTSHORNE, Ample Subvarieties of Algebraic Varieties (Lecture Notes in Mathematics, n° 156, Springer-Verlag, Berlin, 1970). Zbl0208.48901MR44 #211
  10. [10] I. MORRISON, Projective Stability of Ruled Surfaces (Invent. Math., Vol. 56, 1980, pp. 269-304). Zbl0423.14005MR81c:14007
  11. [11] D. MUMFORD, Picard Groups of Moduli Problems, in Arithmetical Algebraic Geometry, O. F. G. SCHILLING Ed., Harper & Row, New York, 1965, pp. 33-81. Zbl0187.42801MR34 #1327
  12. [12] D. MUMFORD, Stability of Projective Varieties (L'Enseignement Math., Vol. 23, 1977, pp. 39-110). Zbl0363.14003MR56 #8568
  13. [13] D. MUMFORD, Towards an Enumerative Geometry of the Moduli Space of Curves, in Arithmetic and Geometry, Vol. 11, M. ARTIN and J. TATE, Eds., Birkhöuser, Boston 1983, pp. 271-328. Zbl0554.14008MR85j:14046
  14. [14] E. VIEHWEG, Weak Positivity and the Additivity of the Kodaira Dimension for Certain Fibre Spaces, in Algebraic Varieties and Analytic Varieties, S. IITAKA, Ed., Adv. Stud. Pure Math., Vol. 1, North-Holland, Amsterdam 1983, pp. 329-353. Zbl0513.14019MR85b:14041
  15. [15] G. XIAO, Fibered Algebraic Surfaces with Low Slope (Math. Ann., Vol. 276, 1987, pp. 449-466). Zbl0596.14028MR88a:14046

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