2018/09/30 by Borys Kadets
Mathematics · Social Sciences · #Algebraic Geometry and Number Theory #Algebraically closed field #Combinatorics #Group (periodic table) #Historical and Political Studies #Hyperplane #Mathematics #Monodromy #Permutation (music) #Permutation group #Physics #Projective space #Projective test #Pure mathematics #Subvariety #Variety (cybernetics) #Vietnamese History and Culture Studies #Zero (linguistics) #math.AG #math.NT
paper · pdf · doi:10.1112/jlms.12375
to appear in Journal of the London Mathematical Society
openalex publication_date 2020/09/07 · arxiv created 2020/11/14 · arxiv updated 2020/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Fix a degree d projective curve X P r over an algebraically closed field K. Let U (P r ) * be a dense open subvariety such that every hyperplane H U intersects X in d smooth points. Varying H U produces the monodromy action : t 1 (U ) S d . Let G X := im(). The permutation group G X is called the sectional monodromy group of X. In characteristic zero G X is always the full symmetric group, but sectional monodromy groups in characteristic p can be smaller. For a large class of space curves (r 3) we classify all possibilities for the sectional monodromy group G as well as the curves with G X = G. We apply similar methods to study a particular family of rational curves in P 2 , which enables us to answer an old question about Galois groups of generic trinomials.