Osaka Journal of Mathematics

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

Xun Yu

Full-text: Open access

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

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1475601823

Mathematical Reviews number (MathSciNet)
MR3554848

Zentralblatt MATH identifier
1352.14021

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

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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