Rational curves of degree at most 9 on a general quintic threefold

Communications in Algebra

Volumn 24, Issue 8, 1996, Pages 2721-2753

  Johnsen, Trygve ^a   Kleiman, Steven L ^a  

^a NONE

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EID: 21344474654     PISSN: 00927872     EISSN: None     Source Type: Journal    
DOI: 10.1080/00927879608542652     Document Type: Article

References (27)

1. E. Arbarello, M. Cornalba, P. Griffiths, and J. Harris, "Algebraic Curves," Grundlehren 267, Springer-Verlag, 1985.
2. 4, Math. Z. 188 (1985), 215-23.
3. P. Candelas, P.S.Green, X.C. de la Ossa, and L. Parkes, A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nuclear Physics. B 358 (1991), 21-74.
4. C. Ciliberto, Hilbert functions of finite sets of points and the genus of a curve in a projective space, in "Space Curves • Proceedings, Rocca di Pappa 1985," F. Ghione, C. Peskine, E. Sernesi (Eds.), Springer Lecture Notes in Math. 1266 (1986), 24-73.
5. H. Clemens, Homological equivalece, modulo algebraic equivalence, is not finitely generated, Publ. Math. I.H.E.S. 58 (1983), 19-38.
6. H. Clemens, Curves on higher-dimensional complex projective manifolds, Proc. International Cong. Math., Berkeley, 1986, 634-40.
7. M. Coppens and T. Johnsen, Secant lines of smooth projective curves, in "Enumerative Algebraic Geometry• Proceedings of the 1989 Zeuthen Symposium," S. L. Kleiman and A. Thorup (Eds.), CONM 123 (1991), 61-87.
8. J. d'Almeida, Courbes de l'espace projectif: Séries linéaires incomplètes et multisécantes, J. reine ang. Math. 370 (1986), 30-51.
9. G. Ellingsrud and S.A. Strømme, The number of twisted cubic curves on the general quintic threefold, Math. Scand. 76 (1995), 5-34.
10. L. Gruson and C. Peskine, Genre des courbes de l'espace projectif, in "Algebraic Geometry • Proceedings, Tromsø, Norway 1977," L. Olsen (Ed.), Springer Lecture Notes in Math. 687 (1978), 31-60.
11. L. Gruson, R. Lazarsfeld, and C. Peskine, On a theorem of Castelnuovo and the equations defining space curves, Invent. Math. 72 (1983), 491-506.
12. M. Guest, On the space of holomorphic maps from the Riemann sphere to the quadric cone., Quart. J. Math. Oxford Ser. (2) 45 (1994), 57-75.
13. R. Hartshorne, "Algebraic Geometry," GTM 52, Springer-Verlag, 1977.
14. A. Hirschowitz, La méthode d'Horace pour línterpolation á plusieurs variables, Manuscripta Math. 50 (1985), 337-88.
15. D. Huybrechts, A note on the finiteness of smooth rational curves on Calabi-Yau threefolds, Preprint, Max-Planck-Institut, April 14, 1993.
16. S. Katz, On the finiteness of rational curves on guintic threefolds, Comp. Math. 60 (1986), 151-62.
17. M. Kontsevich, Enumeration of rational curves via torus actions, Preprint hep-th/9402147.
18. A. Laudal, A generalized trisecant lemma, in "Algebraic Geometry • Proceedings, Tromsø, Norway 1977," L. Olsen (Ed.), Springer Lecture Notes in Math. 687 (1978), 112-49.
19. B. Lian and S.-T. Yau, Arithmetic Properties of Mirror Map and Quantum Coupling, Preprint hep-th/9411234.
20. A. Libgober and J.Teitelbaum, Lines on Calabi-Yau complete intersections, mirror symmetry and Picard-Fuchs equations, Duke Math. J. 69(1) (1993), 29-39.
21. P. Nijsse, Clemens' conjecture for octic and nonic curves, Preprint, U. Leiden, 1993, to appear in Indag. Math.
22. K. Oguiso, Two remarks on Calabai-Yau Moishezon threefolds, Preprint MPI 93-15.
23. n par le fibré tangent restreint, C. R. Acad. Sci. Paris 311 (1990), 181-4.
24. J. Rathmann, The uniform position principle for curves in characteristic p, Math. Ann. 276 (1987), 565-79.
25. I. Vainsencher, Enumeration of n-fold tangent hyperplanes to a surface, J. Alg. Geom. 4 (1995), 503-26.
26. 2n, in "Group Theoretical Methods in Physics • Proceedings, Istanbul, Turkey," Springer Lecture Notes in Physics 180 (1983), 136-41.
27. R. Westhoff, Curves and normal functions on higher dimensional complex varieties, PhD Thesis, U. Utah, June 1993.