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On the finiteness of rational curves on quintic threefolds. (English) Zbl 0606.14039
For any positive integer $$d\leq 7$$, the scheme of smooth rational curves of degree $$d$$ on a generic quintic 3-fold is proved to be non-empty, finite and reduced. Moreover, the number of smooth conics (the case $$d=2)$$ is computed to be 609,250 (the number of lines has been computed by J. Harris).
Reviewer: T.Fujita

##### MSC:
 14N10 Enumerative problems (combinatorial problems) in algebraic geometry 14J30 $$3$$-folds 14C05 Parametrization (Chow and Hilbert schemes)
##### Keywords:
algebraic cycle; quintic 3-fold; number of smooth conics
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##### References:
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