Duke Mathematical Journal

Cycles representing the top Chern class of the Hodge bundle on the moduli space of abelian varieties

Torsten Ekedahl and Gerard van der Geer

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Abstract

We give a generalization to higher genera of the famous formula 12 λ = δ for genus 1

Article information

Source
Duke Math. J., Volume 129, Number 1 (2005), 187-199.

Dates
First available in Project Euclid: 15 July 2005

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1121448868

Digital Object Identifier
doi:10.1215/S0012-7094-04-12917-3

Mathematical Reviews number (MathSciNet)
MR2155061

Zentralblatt MATH identifier
1090.14002

Subjects
Primary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]
Secondary: 14K10: Algebraic moduli, classification [See also 11G15] 14G35: Modular and Shimura varieties [See also 11F41, 11F46, 11G18]

Citation

Ekedahl, Torsten; van der Geer, Gerard. Cycles representing the top Chern class of the Hodge bundle on the moduli space of abelian varieties. Duke Math. J. 129 (2005), no. 1, 187--199. doi:10.1215/S0012-7094-04-12917-3. https://projecteuclid.org/euclid.dmj/1121448868


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References

  • A. Borel and J.-P. Serre, Le théorème de Riemann-Roch, Bull. Soc. Math. France 86 (1958), 97--136.
  • T. Ekedahl and G. van der Geer, The order of the top Chern class of the Hodge bundle on the moduli space of abelian varieties, Acta Math. 192 (2004), 95--109.
  • --------, Cycle classes of the E-O stratification on the moduli of abelian varieties, preprint.
  • H. Esnault and E. Viehweg, Chern classes of Gauss-Manin bundles of weight $1$ vanish, $K$-Theory 26 (2002), 287--305.
  • G. Faltings and C.-L. Chai, Degeneration of Abelian Varieties, Ergeb. Math. Grenzgeb. (3) 22, Springer, Berlin, 1990.
  • W. Fulton, Intersection Theory, Ergeb. Math. Grenzgeb. (3) 2, Springer, Berlin, 1984.
  • G. van der Geer, The Chow ring of the moduli space of abelian threefolds, J. Algebraic Geom. 7 (1998), 753--770.
  • --. --. --. --., ``Cycles on the moduli space of abelian varieties'' in Moduli of Curves and Abelian Varieties: The Dutch Intercity Seminar on Moduli, Aspects Math. E33, Vieweg, Braunschweig, Germany, 1999, 65--89.
  • S. Keel and L. Sadun, Oort's conjecture for $A_g \otimes \mathbbC$, J. Amer. Math. Soc. 16 (2003), 887--900.
  • N. Koblitz, $p$-adic variation of the zeta-function over families of varieties defined over finite fields, Compositio Math. 31 (1975), 119--218.
  • A. Kresch, Cycle groups for Artin stacks, Invent. Math. 138 (1999), 495--536.
  • G. Laumon and L. Moret-Bailly, Champs algébriques, Ergeb. Math. Grenzgeb. (3) 39, Springer, Berlin, 2000.
  • D. Mumford, ``Picard groups of moduli problems'' in Arithmetical Algebraic Geometry (West Lafayette, Ind., 1963), Harper and Row, 1965, 33--81.
  • --------, Stability of Projective Varieties, Monogr. Enseign. Math. 24, Enseignement Math., Geneva, 1977.
  • --. --. --. --., ``On the Kodaira dimension of the Siegel modular variety'' in Algebraic Geometry: Open Problems (Ravello, Italy, 1982), Lecture Notes in Math. 997, Springer, Berlin, 1983, 348--375.
  • --. --. --. --., ``Towards an enumerative geometry of the moduli space of curves'' in Arithmetic and Geometry, Vol. II, Progr. Math. 36, Birkhäuser, Boston, 1983, 271--328.
  • F. Oort, ``Complete subvarieties of moduli spaces'' in Abelian Varieties (Egloffstein, Germany, 1993), de Gruyter, Berlin, 1995, 225--235.