Osaka Journal of Mathematics

On Castelnuovo theory and non-existence of smooth isolated curves in quintic threefolds

Xun Yu

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We find some necessary conditions for a smooth irreducible curve $C\subset \mathbb{P}^{4}$ to be isolated in a smooth quintic threefold. As an application, we prove that Knutsen's list of examples of smooth isolated curves in general quintic threefolds is complete up to degree 9.

Article information

Osaka J. Math. Volume 53, Number 4 (2016), 911-918.

First available in Project Euclid: 4 October 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H45: Special curves and curves of low genus
Secondary: 14H50: Plane and space curves 14J32: Calabi-Yau manifolds 14N25: Varieties of low degree


Yu, Xun. On Castelnuovo theory and non-existence of smooth isolated curves in quintic threefolds. Osaka J. Math. 53 (2016), no. 4, 911--918.

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