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- W2014673913 abstract "ABSTRACT. We prove the following form of the Clemens conjecture in low degree. Let d ≤ 9, and let F be a general quintic threefold in P 4. Then (1) the Hilbert scheme of rational, smooth and irreducible curves of degree d on F is finite, nonempty, and reduced; moreover, each curve is embedded in F with normal bundle (−1) ⊕ (−1), and in P 4 with maximal rank. (2) On F, there are no rational, singular, reduced and irreducible curves of degree d, except for the 17,601,000 six-nodal plane quintics (found by Vainsencher). (3) On F, there are no connected, reduced and reducible curves of degree d with rational components." @default.
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- W2014673913 date "1996-01-01" @default.
- W2014673913 modified "2023-09-26" @default.
- W2014673913 title "Rational curves of degree at most 9 on a general quintic threefold" @default.
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- W2014673913 doi "https://doi.org/10.1080/00927879608542652" @default.
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