1995/05/29 by Atanas Iliev, Iliev, Atanas
Mathematics · Physics and Astronomy · #14E05 (Secondary) #14J45 (Primary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Nonlinear Waves and Solitons #alg-geom #math.AG #msc:14E05 #msc:14J45
paper · pdf · doi:10.48550/arxiv.alg-geom/9505032
Duke preprint, 52 pages, LaTex 2.09
arxiv created 1995/05/29 · openalex publication_date 1995/05/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Among smooth non-rational Fano 3-folds, the non-hyperelliptic Fano 3-fold X(10) of genus 6 has the unique property to admit a non-trivial orbit of birationally isomorphic 3-folds, inside its moduli space. Here we prove that these orbits are, in fact, the same as the fibers of the Griffiths period map for X(10). This leads upto the main result of the paper: The general fiber of the period map for X(10) is a union of two irreducible families of 3-folds: F(1) + F(2), each F(i) -- isomorphic to the Fano surface of conics of any of its elements. As an application, we give a negative answer to a Tjurin's conjecture: The general X(10) is birational to a quartic double solid.