2023/04/19 by А. А. Кузнецова, Kuznetsova, Alexandra
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2304.09955
openalex publication_date 2023/04/19 · openalex created_date 2023/04/24 · openalex updated_date 2026/07/28
We study obstructions to rationality on a nodal Fano threefold M that is a double cover of a smooth quadric threefold ramified over an intersection with a quartic threefold in ℙ4. We prove that if M admits an Artin--Mumford obstruction to rationality then it lies in one of three explicitly described families. Conversely, a general element of any of these families admits an Artin--Mumford obstruction to rationality. Only one of these three families was known before; other two families of nodal Fano threefolds with obstructions to rationality are new.