2016/01/31 by Daniel Allcock
Computer Science · Mathematics · #Algebra over a field #Algebraic Geometry and Number Theory #Algebraically closed field #Automorphism #Combinatorics #Commutative Algebra and Its Applications #Congruence (geometry) #Generality #Geometry #Isometry (Riemannian geometry) #Lattice (music) #Mathematical analysis #Mathematical proof #Mathematics #Physics #Polynomial and algebraic computation #Pure mathematics #Upper and lower bounds #math.AG #msc:14J28 #msc:20F55
paper · pdf · doi:10.1112/jlms.12113
Minor corrections, and a terminology change: "nodal class"--->"nodality class"
arxiv created 2018/02/12 · openalex publication_date 2018/03/28 · arxiv updated 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We give conceptual proofs of some results on the automorphism group of an Enriques surface X, for which only computational proofs have been available. Namely, there is an obvious upper bound on the image of Aut X in the isometry group of the numerical lattice of X, and we establish a lower bound for the image that is quite close to this upper bound. These results apply over any algebraically closed field, provided that X lacks nodal curves, or that all its nodal curves are (numerically) congruent to each other mod 2. In this generality these results were originally proven by Looijenga and Cossec–Dolgachev, developing earlier work of Coble.