On smooth and isolated curves in general complete intersection Calabi-Yau threefolds

2012/08/30 by Xun Yu, Yu Xun, Yu, Xun
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.1208.6282

30 pages

arxiv created 2012/08/30 · openalex publication_date 2012/08/30 · arxiv updated 2012/08/31 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Recently Knutsen found criteria for the curves in a complete linear system |L| on a smooth surface X in a nodal K-trivial threefold Y₀ to deform to a scheme of finitely many smooth isolated curves in a general deformation Y_t of Y₀. In this article we develop new methods to check whether the set of nodes of Y₀ imposes independent conditions on |L|. As an application, we find new smooth isolated curves in complete intersection Calabi-Yau threefolds.

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