1999/06/01 by Keiji Oguiso, K. Oguiso, De‐Qi Zhang +3
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG
paper · pdf · doi:10.48550/arxiv.math/9906005
22 pages. Math. Z. to appear
arxiv created 1999/06/01 · openalex publication_date 1999/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that there are exactly, up to isomorphisms, seven extremal log Enriques surfaces Z and construct all of them; among them types D19 and A19 have been shown of certain uniqueness by M. Reid. We also prove that the (degree 3 or 2) canonical covering of each of these seven Z has either X3 or X4 as its minimal resolution. Here X3 (resp. X4) is the unique K3 surface with Picard number 20 and discriminant 3 (resp. 4), which are called the most algebraic K3 surfaces by Vinberg and have infinite automorphism groups (by Shioda-Inose and Vinberg).