2001/10/19 by Andreas Leopold Knutsen, Knutsen, Andreas Leopold
Mathematics · #14J32 (Primary) 14J28 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.AG #msc:14J28 #msc:14J32
paper · pdf · doi:10.48550/arxiv.math/0110220
18 pages. The previous version of the preprint used a result from a published paper that turned out to have a gap. The gap has been fixed in another paper, so finally the results of this preprint have a complete proof. Moreover, the whole preprint has been rewritten, with some simplified proofs
openalex publication_date 2001/10/19 · arxiv created 2012/09/05 · arxiv updated 2012/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show the existence of smooth isolated curves of different degrees and genera in Calabi-Yau threefolds that are complete intersections in homogeneous spaces. Along the way, we classify all degrees and genera of smooth curves on BN general K3 surfaces of low genera. By results of Mukai, these are the K3 surfaces that can be realised as complete intersections in certain homogeneous spaces.