On the Complete Classification of Extremal Log Enriques Surfaces
نویسندگان
چکیده
We show that there are exactly, up to isomorphisms, seven rational 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).
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