Arkiv för Matematik

On a problem of Griffiths: An inversion of Abel’s theorem for families of zero-cycles

Bruno Fabre

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Abstract

This paper gives a partial answer to a problem raised by Griffiths in [4], which is a kind of converse of Abel’s theorem.

Article information

Source
Ark. Mat., Volume 41, Number 1 (2003), 61-84.

Dates
Received: 12 December 2001
Revised: 11 July 2002
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898791

Digital Object Identifier
doi:10.1007/BF02384567

Mathematical Reviews number (MathSciNet)
MR1971940

Zentralblatt MATH identifier
1035.14002

Rights
2003 © Institut Mittag-Leffler

Citation

Fabre, Bruno. On a problem of Griffiths: An inversion of Abel’s theorem for families of zero-cycles. Ark. Mat. 41 (2003), no. 1, 61--84. doi:10.1007/BF02384567. https://projecteuclid.org/euclid.afm/1485898791


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References

  • Barlet, D., Le faisceau ω (X) sur un espace analytique X dimension pure, in Fonctions de plusieurs variables complexes III (Sém. François Norguet. 1975–1977), Lecture Notes in Math. 670, pp. 187–204, Springer-Verlag, Berlin-Heidelberg, 1978.
  • Ciliberto, C., Alcune applicazioni di un classico procedimento di Castelnuovo, Pubbl. Ist. Mat. “R. Caccioppoli” Univ. Napoli 39, Naples, 1983.
  • Ciliberto, C. and Lazarsfeld, R., On the uniqueness of certain linear series on some classes of curves, in Complete Intersections (Acireale, 1983) (Greco, S. and Strano, R., eds.), Lecture Notes in Math. 1092, pp. 198–213, Springer-Verlag, Berlin-Heidelberg, 1983.
  • Griffiths, P., On Abel’s differential equations V, in Algebraic Geometry (Baltimore, Md., 1976) (Igusa, J.-I., ed.), pp. 26–51, Johns Hopkins Univ. Press, Baltimore, Md., 1977.
  • Griffiths, P. and Harris, J., Principles of Algebraic Geometry, Wiley, New York, 1978.
  • Henkin, G. and Passare, M., Holomorphic forms on singular varieties and variations on Lie-Griffiths theorem, Invent. Math. 135 (1999), 297–328.
  • Herrera, M. E. and Liebermann, D. I., Residues and principal values on complex spaces, Math. Ann. 194 (1971), 259–294.
  • Kaddar, M., Integration sur les cycles et formes de type L2, C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), 663–668.
  • Remmert, R., Holomorphe und meromorphe Abbildungen komplexer Räume, Math. Ann. 133 (1957), 328–370.
  • Rosenlicht, M., Equivalence relations on algebraic curves, Ann. of Math. 58 (1952), 169–191.
  • Rosenlicht, M., Generalized Jacobian varieties, Ann. of Math. 59 (1954), 505–530.
  • Schwartz, L., Théorie des distributions, 2nd ed., Hermann, Paris, 1966.