Rigid Curves in Complete Intersection Calabi-Yau Threefolds

Compositio Mathematica

Volumn 123, Issue 2, 2000, Pages 185-208

  Kley, Holger P ^a  

^a UNIVERSITY OF UTAH   (United States)

Author keywords

Calabi Yau threefolds; Hilbert schemes; K3 surfaces

Indexed keywords

EID: 0009914198     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1002012414149     Document Type: Article

References (23)

1. Altman, A. and Kleiman, S.: Introduction to Grothendieck Duality Theory, Lecture Notes in Math. 146, Springer, New York, 1970.
2. Atiyah, M. F.: Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 86 (1957), 181-207.
3. Bershadsky, M., Cecotti, S., Ooguri, M. and Vafa, V.: Holomorphic anomalies in topological field theories, Nuclear Phys. B 405 (1993), 279-304.
4. Candelas, P., Green, P. S., de la Ossa, X. C. and Vafa, C.: A pair of Calabi-Yau manifolds as an exactly soluble superconformal theory, Nuclear Phys. B 359 (1991), 21-74.
5. Clemens, H.: Homological equivalence, modulo algebraic equivalence, is not finitely generated, Inst. Hautes Études Sci. Publ. Math. 58 (1983), 19-38.
6. Clemens, H.: Curves on higher-dimensional complex projective manifolds, In: Proc. Internat. Congr. Math. (1986: Berkeley), Amer. Math. Soc., Providence, 1987, pp. 634-640.
7. Ekedahl, T. Johnsen, T. and Sommervoll, D. E.: Isolated rational curves on K3-fibered Calabi-Yau threefolds, Preprint, alg-geom9710010.
8. Ellingsrud, G. and Strømme, S. A.: Bott's formula and enumerative geometry, J. Amer. Math. Soc. 9 (1996), 175-194.
9. Fulton, W.: Intersection Theory, Ergeb. Math. Grenzgeb. (3)2, Springer, Berlin, 1984.
10. 1,4 and elliptic Gromov-Witten invariants, J. Amer. Math. Soc. 10(4) (1997), 973-998.
11. Givental, A. B.: Equivariant Gromov-Witten invariants, Internat. Math. Res. Notices 1996(13) (1996), 613-663.
12. Gruson, L., Lazarsfeld, R. and Peskine, C.: On a theorem of Castelnuovo, and the equations defining space curves, Invent. Math. 72 (1983), 491-506.
13. Johnsen, T. and Kleiman, S. L.: Rational curves of degree at most 9 on a general quintic threefold, Comm. Algebra 24(8) (1996), 2721-2753.
14. Katz, S.: On the finiteness of rational curves on quintic threefolds, Compositio Math. 60 (1986), 151-162.
15. Knutsen, A. L.: On degrees and genera of smooth curves on projective K3 surfaces, Preprint, math.AG9805140, 1998.
16. Kollár, J.: Rational curves on algebraic varieties, Ergeb. Math. Grenzgeb. (3) 32, Springer, Berlin, 1996.
17. Kontsevich, M. L.: Enumeration of rational curves via torus actions, In: The Moduli Space of Curves (Texel Island, 1994), Progr. Math. 129, Birkäuser, Basel, 1995, pp. 335-368.
18. Libgober, A. and Teitelbaum, J.: Lines on Calabi-Yau complete intersections, mirror symmetry, and Picard-Fuchs equations, Duke Math. J. (1993), 29-39.
19. 3, Nagoya Math. J. 96 (1984), 127-132.
20. Mumford, D.: Abelian Varieties, Tata Inst. Fund. Res. Stud. Math. 5, Oxford Univ. Press, 1974.
21. Nijsse, P. G. J.: Clemens' conjecture for octic and nonic curves, Indag. Math. (N. S.) 6(2) (1995), 213-221.
22. Oguiso, K.: Two remarks on Calabi-Yau Moishezon threefolds, J. reine angew. Math. 452 (1994), 153-161.
23. Sernesi, E.: Topics on Families of Projective Schemes, Queen's Papers in Pure and Appl. Math. 73, Queen's Univ. Press, Kingston, ON, 1986.