2000/05/04 by Atanas Iliev, Iliev, Atanas, Carmen Schuhmann +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.math/0005040
19 pages, Latex
arxiv created 2000/05/04 · openalex publication_date 2000/05/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove that any smooth prime Fano threefold, different from the Mukai-Umemura threefold, contains a 1-dimensional family of intersecting lines. Combined with a result of the second author (see J. Algebr. Geom. 8:2 (1999), 221-244) this implies that any morphism from a smooth Fano threefold of index 2 to a smooth Fano threefold of index 1 must be constant, which gives an answer in dimension 3 to a question stated by Peternell.