On the complete classification of extremal log Enriques surfaces

Details On the complete classification of extremal log Enriques surfaces On the complete classification of extremal log Enriques surfaces

1999-06-01

arxiv.org/abs/math/9906005v1

Mathematics

Algebraic Geometry

22 pages. Math. Z. to appear

Scientific paper

We show that there are exactly, up to isomorphisms, seven extremal log Enriques surfaces Z and construct all of them; among them types D_{19} and A_{19} 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 X_3 or X_4 as its minimal resolution. Here X_3 (resp. X_4) 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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