On the finiteness of rational curves on quintic threefolds

Sheldon Katz

Compositio Mathematica (1986)

  • Volume: 60, Issue: 2, page 151-162
  • ISSN: 0010-437X

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Katz, Sheldon. "On the finiteness of rational curves on quintic threefolds." Compositio Mathematica 60.2 (1986): 151-162. <http://eudml.org/doc/89802>.

@article{Katz1986,
author = {Katz, Sheldon},
journal = {Compositio Mathematica},
keywords = {algebraic cycle; quintic 3-fold; number of smooth conics},
language = {eng},
number = {2},
pages = {151-162},
publisher = {Martinus Nijhoff Publishers},
title = {On the finiteness of rational curves on quintic threefolds},
url = {http://eudml.org/doc/89802},
volume = {60},
year = {1986},
}

TY - JOUR
AU - Katz, Sheldon
TI - On the finiteness of rational curves on quintic threefolds
JO - Compositio Mathematica
PY - 1986
PB - Martinus Nijhoff Publishers
VL - 60
IS - 2
SP - 151
EP - 162
LA - eng
KW - algebraic cycle; quintic 3-fold; number of smooth conics
UR - http://eudml.org/doc/89802
ER -

References

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  1. [1] H. Clemens: Homological equivalence, modulo algebraic equivalence, is not finitely generated. Publ. Math IHES58 (1983) 19-38. Zbl0529.14002MR720930
  2. [2] H. Clemens: Some results on Abel-Jacobi mappings. In: Topics in transcendental algebraic Geometry. Princeton Univ. Press:Princeton, NJ (1984). Zbl0575.14007
  3. [3] A. Collino, J. Murre and G. Welters: On the family of conics lying on a quartic threefold. Rend. Sem. Mat. Univ. Pol. Torino38 (1980). Zbl0474.14023MR608936
  4. [4] P. Griffiths and J. Harris: Principles of algebraic Geometry. Wiley: New York (1978). Zbl0408.14001MR507725
  5. [5] L. Gruson, R. Lazarsfeld and C. Peskine: On a theorem of Castelnuovo and the equations defining space curves. Inv. Math.72 (1983) 491-506. Zbl0565.14014MR704401
  6. [6] J. Harris: Galois groups of enumerative problems. Duke Math. Jour.46 (1979) 685-724. Zbl0433.14040MR552521
  7. [7] R. Hartshorne: Algebraic Geometry. Springer-Verlag:New York (1977). Zbl0367.14001MR463157
  8. [8] S. Katz: Degenerations of quintic threefolds and their lines. Duke Math. Jour.50 (1983) 1127-1135. Zbl0616.14035MR726321
  9. [9] S. Katz: Lines on complete intersection threefolds with K = 0, to appear in Math. Zeit. Zbl0563.14020
  10. [10] H. Matsumura: Commutative Algebra. Benjamin/Cummings:Reading, Mass. (1980). Zbl0441.13001MR575344
  11. [11] S. Mori: On degrees and genera of curves on smooth quartic surfaces in P3. Nagoya Math. Jour.96 (1984). Zbl0576.14032MR771073
  12. [12] 1. PETROVSKII and S. NIKOLSKI, eds: Algebraic surfaces. Proc. Steklov Inst. Math.75 (1965) AMS, Prov. RI1967. 

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