2019/09/04 by Xavier Roulleau, Roulleau, Xavier
Arts and Humanities · Mathematics · #14J28 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Historical Studies and Socio-cultural Analysis
paper · pdf · doi:10.48550/arxiv.1909.01909
openalex publication_date 2019/09/04 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
Nikulin and Vinberg proved that there are only a finite number of lattices of rank ≥ 3 that are the Néron-Severi group of projective K3 surfaces with a finite automorphism group. The aim of this paper is to provide a more geometric description of such K3 surfaces X, when these surfaces have moreover no elliptic fibrations. In that case we show that such K3 surface is either a quartic with special hyperplane sections or a double cover of the plane branched over a smooth sextic curve which has special tangencies properties with some lines, conics or cuspidal cubic curves. We then study the converse i.e. if the geometric description we obtained characterizes these surfaces. In 4 cases the description is sufficient, in each of the 4 other cases there is exactly another one possibility which we study. We obtain that at least 5 moduli spaces of K3 surfaces (among the 8 we study) are unirational.