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A076912 Number of degree-n rational curves on a general quintic. 4
5, 2875, 609250, 317206375, 242467530000, 229305888887625, 248249742118022000, 295091050570845659250, 375632160937476603550000, 503840510416985243645106250 (list; graph; refs; listen; history; text; internal format)



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.

Ellingsrud, Geir and Stromme, Stein Arild, The number of twisted cubic curves on the general quintic threefold (preliminary version). In Essays on Mirror Manifolds, 181-222, Int. Press, Hong Kong, 1992.

Ellingsrud, Geir and Stromme, Stein Arild, The number of twisted cubic curves on the general quintic threefold.  Math. Scand. 76 (1995), no. 1, 5-34.

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.


Table of n, a(n) for n=0..9.

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.

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

Steven R. Finch, Enumerative geometry, February 24, 2014. [Cached copy, with permission of the author]

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.

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.

Shing-Tung Yau and Steve Nadis, String Theory and the Geometry of the Universe's Hidden Dimensions, Notices Amer. Math. Soc., 58 (Sep 2011), 1067-1076.


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


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

Sequence in context: A274527 A258980 A096934 * A060041 A199878 A076908

Adjacent sequences:  A076909 A076910 A076911 * A076913 A076914 A076915




N. J. A. Sloane, Nov 28 2002



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Last modified June 24 01:31 EDT 2017. Contains 288697 sequences.