This site is supported by donations to The OEIS Foundation.



Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A076912 Number of degree-n rational curves on a general quintic. 3
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.

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

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.

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.


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.

S. Finch, Enumerative geometry.

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.


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: A036772 A117011 A096934 * A060041 A199878 A060345

Adjacent sequences:  A076909 A076910 A076911 * A076913 A076914 A076915




N. J. A. Sloane, Nov 28 2002



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 21 13:45 EST 2014. Contains 252321 sequences.