https://hal.inria.fr/hal-03046866Artebani, MichelaMichelaArtebaniDeisler, Claudia CorreaClaudia CorreaDeislerRoulleau, XavierXavierRoulleauAMU - Aix Marseille UniversitéMori dream K3 surfaces of Picard number four: projective models and Cox ringsHAL CCSD2022[MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG]Roulleau, Xavier2020-12-08 15:55:062022-06-28 10:04:362020-12-08 15:55:06enJournal articles1In this paper we study the geometry of the $14$ families of K3 surfaces of Picard number four with finite automorphism group, whose N\'eron-Severi lattices have been classified by \`E.B. Vinberg. We provide projective models, we identify the degrees of a generating set of the Cox ring and in some cases we prove the unirationality of the associated moduli space.