## Osaka Journal of Mathematics

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

Xun Yu

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 4 October 2016

https://projecteuclid.org/euclid.ojm/1475601823

Mathematical Reviews number (MathSciNet)
MR3554848

Zentralblatt MATH identifier
1352.14021

#### Citation

Yu, Xun. On Castelnuovo theory and non-existence of smooth isolated curves in quintic threefolds. Osaka J. Math. 53 (2016), no. 4, 911--918.https://projecteuclid.org/euclid.ojm/1475601823

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