On Castelnuovo theory and non-existence of smooth isolated curves in quintic threefolds
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Publication:342965
zbMath1352.14021arXiv1302.5410MaRDI QIDQ342965
Publication date: 18 November 2016
Published in: Osaka Journal of Mathematics (Search for Journal in Brave)
Abstract: We give some necessary conditions for a smooth irreducible curve $Csubset mathbb{P}^4$ to be isolated in a smooth quintic threefold, and also find a lower bound for $h^1(mathcal{N}_{C/{mathbb{P}^4}})$. Combining these with beautiful results in Castelnuovo theory, we prove certain non-existence results on smooth curves in smooth quintic threefolds. As an application, we can prove Knutsen's list of examples of smooth isolated curves in general quintic threefolds is complete up to degree 9.
Full work available at URL: https://arxiv.org/abs/1302.5410
Plane and space curves (14H50) Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Varieties of low degree (14N25)
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