2023/02/19 by Frank Gounelas, Gounelas, Frank, Alexis Kouvidakis +1
Mathematics · #11D41 #14J30 #14J35 #14J70 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2302.09562
openalex publication_date 2023/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study properties of the locus of second type lines of a general cubic threefold and fourfold. By analysing the geometry of the Fano scheme of lines of the Fermat cubic fourfold and in particular giving an explicit description of the locus of second type lines, we deduce that the Voisin map is birational over the second type locus. For a general cubic threefold, by studying properties of the second type locus again, we compute that various natural geometric monodromy groups are the full symmetric group.