Journal of Differential Geometry

On a conjecture of Clemens on rational curves on hypersurfaces

Claire Voisin

Full-text: Open access

Article information

Source
J. Differential Geom., Volume 44, Number 1 (1996), 200-213.

Dates
First available in Project Euclid: 26 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.jdg/1214458743

Digital Object Identifier
doi:10.4310/jdg/1214458743

Mathematical Reviews number (MathSciNet)
MR1420353

Zentralblatt MATH identifier
0883.14022

Subjects
Primary: 14J70: Hypersurfaces
Secondary: 14H99: None of the above, but in this section

Citation

Voisin, Claire. On a conjecture of Clemens on rational curves on hypersurfaces. J. Differential Geom. 44 (1996), no. 1, 200--213. doi:10.4310/jdg/1214458743. https://projecteuclid.org/euclid.jdg/1214458743


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References

  • [1] M.Chang and Z.Ran, Divisors onsome generic hypersurfaces, J. Differential Geom. 38 (1993) 671-678.
  • [2] H. Clemens, Curves in generic hypersurfaces, Ann. Sci. Ecole Norm. Sup. 19 (1986) 629-636.
  • [3] L. Ein, Subvarieties of generic complete intersections, Invent. Math. 94 (1988) 163-169.
  • [4] L. Ein, Subvarieties ofgeneric complete intersections. II, Math. Ann. 289 (1991) 465-471.
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  • [6] M. Green, Koszul cohomology and thegeometry of protective varieties, J. Differential Geom. 20 (1984) 279-289.
  • [7] A.Lopez and G-P. Pirola, Onthe curves through ageneral point of a smooth surface in P3, Preprint, 1993.
  • [8] M. Nori, Algebraic cycles and Hodge theoretic connectivity, Invent. Math. I l l (2)(1993) 349-373.
  • [9] C. Voisin, Variations destructure deHodge et zero-cycles sur lessurfaces generates, Math. Ann. 299 (1994) 77-103.
  • [10] C. Voisin, Uneremarque sur invariant infinitesimal desfonctions normales, C.R.Acad. Sci. Paris Serie I, 307 (1988) 157-160.
  • [11] G. Xu, Subvarieties of general hypersurfaces inprotective space, J. Differential Geom. 39 (1994) 139-172.
  • [12] G. Xu, Divisors on generic complete intersections in protective space, Preprint, 1994.

Corrections

  • See Correction: Claire Voisin. A correction: ``On a conjecture of Clemens on rational curves on hypersurfaces''. J. Differential Geom., Volume 49, Number 3, (1998), 601--611.