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2016•Osaka City University (Osaka City University)Open access

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

Xun Yu

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Abstract

Abstract. We give some necessary conditions for a smooth irreducible curve C ⊂ P4 to be isolated in a smooth quintic threefold, and also find a lower bound for h1(NC/P4). 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. 1.

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Abstract. We give some necessary conditions for a smooth irreducible curve C ⊂ P4 to be isolated in a smooth quintic threefold, and also find a lower bound for h1(NC/P4). 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. 1.

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Abstract. We give some necessary conditions for a smooth irreducible curve C ⊂ P4 to be isolated in a smooth quintic threefold, and also find a lower bound for h1(NC/P4). 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. 1.

Key concepts: Quintic function, Mathematics, Degree (music), Pure mathematics, Nonlinear system, Physics, Quantum mechanics, Acoustics

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