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A076912 Number of degree-n rational curves on a general quintic. +0
3
5, 2875, 609250, 317206375, 242467530000, 229305888887625, 248249742118022000, 295091050570845659250, 375632160937476603550000, 503840510416985243645106250 (list; graph; listen)
OFFSET

0,1

COMMENT

An expert tells me that this sequence (unlike A060041) is ill-defined for n >= 10.

REFERENCES

J. Bertin and C. Peters, Variations of Hodge structure ..., pp. 151-232 of J. Bertin et al., eds., Introduction to Hodge Theory, Amer. Math. Soc. and Soc. Math. France, 2002; see p. 220.

P. Candelas et al., A pair of Calabi-yau manifolds as an exactly soluble superconformal theory, Nuclear Phys. B 359 (1991), 21-74.

D. A. Cox and S. Katz, Mirror Symmetry and Algebraic Geometry, Amer. Math. Soc., 1999.

Trygve Johnsen and Steven L. Kleiman, Rational curves of degree at most 9 on a general quintic threefold, arXiv:alg-geom/9510015.

Trygve Johnsen and Steven L. Kleiman, Toward Clemens' Conjecture in degrees between 10 and 24, arXiv:alg-geom/9601024.

B. Mazur, Perturbations, deformations and variations ..., Bull. Amer. Math. Soc., 41 (2004), 307-336.

R. Pandharipande, Rational curves on hypersurfaces (after A. Givental), Seminaire Bourbaki, Vol. 1997/98. Asterisque No. 252 (1998), Exp. No. 848, 5, 307-340.

Ellingsrud, Geir and Stromme, Stein Arild, Bott's formula and enumerative geometry. J. Amer. Math. Soc. 9 (1996), 175-193. [arXiv:alg-geom/9411005]

LINKS

V. Batyrev, Review of "Mirror Symmetry and Algebraic Geometry", by D. A. Cox and S. Katz, Bull. Amer. Math. Soc., 37 (No. 4, 2000), 473-476.

David R. Morrison, Mathematical Aspects of Mirror Symmetry, in Complex Algebraic Geometry (J. Koll\'ar, ed.), IAS/Park City Math. Series, vol. 3, 1997, pp. 265-340

EXAMPLE

a(1) = 2875 = number of lines in the quintic.

CROSSREFS

Coincides with A060041 for n <= 9, but possibly not for n = 10. Cf. A060345, A076913.

Sequence in context: A036772 A117011 A096934 this_sequence A060041 A060345 A076908

Adjacent sequences: A076909 A076910 A076911 this_sequence A076913 A076914 A076915

KEYWORD

nonn

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com), Nov 28 2002

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Last modified December 17 19:39 EST 2009. Contains 170821 sequences.


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