On isolated smooth curves of low genera in Calabi-Yau complete intersection threefolds

2010/09/22 by Andreas Leopold Knutsen, Knutsen, Andreas Leopold
Mathematics · #Advanced Algebra and Geometry #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.1009.4419

22 pages, to appear in Transactions of the AMS

arxiv created 2010/09/22 · openalex publication_date 2010/09/22 · arxiv updated 2010/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Building on results of Clemens and Kley, we find criteria for a continuous family of curves 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. As an application, we show the existence of smooth isolated curves of bounded genera and unbounded degrees in Calabi-Yau complete intersections threefolds.

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