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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)
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References:
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