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A076912
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Number of degree-n rational curves on a general quintic threefold.
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5
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5, 2875, 609250, 317206375, 242467530000, 229305888887625, 248249742118022000, 295091050570845659250, 375632160937476603550000, 503840510416985243645106250, 704288164978454686113382643750
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OFFSET
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0,1
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REFERENCES
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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.
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.
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LINKS
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Steven R. Finch, Enumerative geometry, February 24, 2014. [Cached copy, with permission of the author]
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EXAMPLE
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a(1) = 2875 = number of lines in the quintic.
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CROSSREFS
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Coincides with A060041 for n <= 9, but not for n = 10.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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a(10) = A060041(10) - 6 * 17601000 added by Andrey Zabolotskiy, Sep 10 2022 (see Encyclopedia of Mathematics, Clemens' conjecture)
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STATUS
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approved
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