Abstract
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.
Citation
Xun Yu. "On Castelnuovo theory and non-existence of smooth isolated curves in quintic threefolds." Osaka J. Math. 53 (4) 911 - 918, October 2016.
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