English

On the complete classification of extremal log Enriques surfaces

Algebraic Geometry 2007-05-23 v1

Abstract

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).

Keywords

Cite

@article{arxiv.math/9906005,
  title  = {On the complete classification of extremal log Enriques surfaces},
  author = {K. Oguiso and D. -Q. Zhang},
  journal= {arXiv preprint arXiv:math/9906005},
  year   = {2007}
}

Comments

22 pages. Math. Z. to appear

R2 v1 2026-07-22T18:03:16.997Z