Duke Mathematical Journal

The Griffiths infinitesimal invariant for a curve in its Jacobian

Alberto Collino and Gian Pietro Pirola
Source: Duke Math. J. Volume 78, Number 1 (1995), 59-88.
First Page: Show Hide
Primary Subjects: 14D07
Secondary Subjects: 14C30, 14H40
Full-text: Access denied (no subscription detected)
We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.
If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077285549
Mathematical Reviews number (MathSciNet): MR1328752
Zentralblatt MATH identifier: 0846.14016
Digital Object Identifier: doi:10.1215/S0012-7094-95-07804-1

References

[1] E. Arbarello and M. Cornalba, On a conjecture of Petri, Comment. Math. Helv. 56 (1981), no. 1, 1–38.
Mathematical Reviews (MathSciNet): MR82k:14029
Zentralblatt MATH: 0505.14002
Digital Object Identifier: doi:10.1007/BF02566195
[2] E. Arbarello, M. Cornalba, P. Griffiths, and J. Harris, Geometry of algebraic curves. Vol. I, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 267, Springer-Verlag, New York, 1985.
Mathematical Reviews (MathSciNet): MR86h:14019
Zentralblatt MATH: 0559.14017
[3] F. Bardelli, A footnote to a paper by A. Grothendieck (the Grothendieck generalized Hodge conjecture for some geometric families of abelian threefolds): “Hodge's general conjecture is false for trivial reasons”, Rend. Sem. Mat. Fis. Milano 57 (1987), 109–124 (1989).
Mathematical Reviews (MathSciNet): MR90k:14049
Zentralblatt MATH: 0701.14005
Digital Object Identifier: doi:10.1007/BF02925045
[4] F. Bardelli, Curves of genus three on a general abelian threefold and the nonfinite generation of the Griffiths group, Arithmetic of complex manifolds (Erlangen, 1988), Lecture Notes in Math., vol. 1399, Springer, Berlin, 1989, pp. 10–26.
Mathematical Reviews (MathSciNet): MR91a:14004
Zentralblatt MATH: 0703.14004
Digital Object Identifier: doi:10.1007/BFb0095965
[5] J. Carlson, M. Green, P. Griffiths, and J. Harris, Infinitesimal variations of Hodge structure. I, Compositio Math. 50 (1983), no. 2-3, 109–205.
Mathematical Reviews (MathSciNet): MR86e:32026a
Zentralblatt MATH: 0531.14006
[6] G. Ceresa, $C$ is not algebraically equivalent to $C\sp-$ in its Jacobian, Ann. of Math. (2) 117 (1983), no. 2, 285–291.
Mathematical Reviews (MathSciNet): MR84f:14005
Zentralblatt MATH: 0538.14024
Digital Object Identifier: doi:10.2307/2007078
[7] H. Clemens, Homological equivalence, modulo algebraic equivalence, is not finitely generated, Inst. Hautes Études Sci. Publ. Math. (1983), no. 58, 19–38 (1984).
Mathematical Reviews (MathSciNet): MR86d:14043
Zentralblatt MATH: 0529.14002
Digital Object Identifier: doi:10.1007/BF02953771
[8] H. Clemens, Some results about Abel-Jacobi mappings, Topics in transcendental algebraic geometry (Princeton, N.J., 1981/1982), Ann. of Math. Stud., vol. 106, Princeton Univ. Press, Princeton, NJ, 1984, pp. 289–304.
Mathematical Reviews (MathSciNet): MR756858
Zentralblatt MATH: 0575.14007
[9] A. Collino, Applications of Griffiths infinitesimal invariant $K$-Theory, in preparation.
[10] E. Colombo and G. Pirola, New cycles in the Griffiths group of the generic abelian threefold, Amer. J. Math. 116 (1994), no. 3, 637–667.
Mathematical Reviews (MathSciNet): MR95d:14007
Zentralblatt MATH: 0817.14002
Digital Object Identifier: doi:10.2307/2374995
[11] W. Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984.
Mathematical Reviews (MathSciNet): MR85k:14004
Zentralblatt MATH: 0541.14005
[12] W. Fulton and J. Harris, Representation theory, Graduate Texts in Mathematics, vol. 129, Springer-Verlag, New York, 1991.
Mathematical Reviews (MathSciNet): MR93a:20069
Zentralblatt MATH: 0744.22001
[13] D. Gieseker, A lattice version of the KP equation, Acta Math. 168 (1992), no. 3-4, 219–248.
Mathematical Reviews (MathSciNet): MR93e:58083
Zentralblatt MATH: 0809.14015
Digital Object Identifier: doi:10.1007/BF02392979
[14] M. Green, Griffiths' infinitesimal invariant and the Abel-Jacobi map, J. Differential Geom. 29 (1989), no. 3, 545–555.
Mathematical Reviews (MathSciNet): MR90c:14006
Zentralblatt MATH: 0692.14003
Project Euclid: euclid.jdg/1214443062
[15] P. Griffiths, Infinitesimal variations of Hodge structure. III. Determinantal varieties and the infinitesimal invariant of normal functions, Compositio Math. 50 (1983), no. 2-3, 267–324.
Mathematical Reviews (MathSciNet): MR86e:32026c
Zentralblatt MATH: 0576.14009
[16]1 P. Griffiths, Periods of integrals on algebraic manifolds. I. Construction and properties of the modular varieties, Amer. J. Math. 90 (1968), 568–626.
Mathematical Reviews (MathSciNet): MR37:5215
Zentralblatt MATH: 0169.52303
Digital Object Identifier: doi:10.2307/2373545
[16]2 P. Griffiths, Periods of integrals on algebraic manifolds. II. Local study of the period mapping, Amer. J. Math. 90 (1968), 805–865.
Mathematical Reviews (MathSciNet): MR38:2146
Zentralblatt MATH: 0183.25501
Digital Object Identifier: doi:10.2307/2373485
[17] B. Harris, Harmonic volumes, Acta Math. 150 (1983), no. 1-2, 91–123.
Mathematical Reviews (MathSciNet): MR84k:32032
Zentralblatt MATH: 0527.30032
Digital Object Identifier: doi:10.1007/BF02392968
[18] M. Nori, Cycles on the generic abelian threefold, Proc. Indian Acad. Sci. Math. Sci. 99 (1989), no. 3, 191–196.
Mathematical Reviews (MathSciNet): MR90k:14003
Zentralblatt MATH: 0725.14006
Digital Object Identifier: doi:10.1007/BF02864390
[19] G. Pirola, On the Abel-Jacobi image of cycles for a generic abelian fourfold, Boll. Un. Mat. Ital. A (7) 8 (1994), no. 1, 83–93.
Mathematical Reviews (MathSciNet): MR95a:14049
Zentralblatt MATH: 0816.14016
[20] G. Pirola, On a conjecture of Xiao, J. Reine Angew. Math. 431 (1992), 75–89.
Mathematical Reviews (MathSciNet): MR93k:14014
Zentralblatt MATH: 0753.14040
Digital Object Identifier: doi:10.1515/crll.1992.431.75
[21] G. Pirola, Abel-Jacobi invariant and curves on generic Abelian varieties, preprint.
Mathematical Reviews (MathSciNet): MR1336610
Zentralblatt MATH: 0837.14036
[22] K. A. Ribet, Hodge classes on cycles of certain types of abelian varieties, Amer. J. Math. 105 (1983), no. 2, 523–538.
Mathematical Reviews (MathSciNet): MR85a:14030
Zentralblatt MATH: 0586.14003
Digital Object Identifier: doi:10.2307/2374267
[23] C. Voisin, Une approche infinitésimale du théorème de H. Clemens sur les cycles d'une quintique générale de $\bf P\sp 4$, J. Algebraic Geom. 1 (1992), no. 1, 157–174.
Mathematical Reviews (MathSciNet): MR92k:14008
Zentralblatt MATH: 0787.14003
[24] G. Xiao, Irregularity of surfaces with a linear pencil, Duke Math. J. 55 (1987), no. 3, 597–602.
Mathematical Reviews (MathSciNet): MR89c:14055
Zentralblatt MATH: 0651.14021
Digital Object Identifier: doi:10.1215/S0012-7094-87-05529-3
Project Euclid: euclid.dmj/1077306165

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?