# On the finiteness of rational curves on quintic threefolds

Compositio Mathematica (1986)

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

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topKatz, 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

top- [1] H. Clemens: Homological equivalence, modulo algebraic equivalence, is not finitely generated. Publ. Math IHES58 (1983) 19-38. Zbl0529.14002MR720930
- [2] H. Clemens: Some results on Abel-Jacobi mappings. In: Topics in transcendental algebraic Geometry. Princeton Univ. Press:Princeton, NJ (1984). Zbl0575.14007
- [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] P. Griffiths and J. Harris: Principles of algebraic Geometry. Wiley: New York (1978). Zbl0408.14001MR507725
- [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] J. Harris: Galois groups of enumerative problems. Duke Math. Jour.46 (1979) 685-724. Zbl0433.14040MR552521
- [7] R. Hartshorne: Algebraic Geometry. Springer-Verlag:New York (1977). Zbl0367.14001MR463157
- [8] S. Katz: Degenerations of quintic threefolds and their lines. Duke Math. Jour.50 (1983) 1127-1135. Zbl0616.14035MR726321
- [9] S. Katz: Lines on complete intersection threefolds with K = 0, to appear in Math. Zeit. Zbl0563.14020
- [10] H. Matsumura: Commutative Algebra. Benjamin/Cummings:Reading, Mass. (1980). Zbl0441.13001MR575344
- [11] S. Mori: On degrees and genera of curves on smooth quartic surfaces in P3. Nagoya Math. Jour.96 (1984). Zbl0576.14032MR771073
- [12] 1. PETROVSKII and S. NIKOLSKI, eds: Algebraic surfaces. Proc. Steklov Inst. Math.75 (1965) AMS, Prov. RI1967.

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