Algebraic surfaces with quotient singularities - including some discussion on automorphisms and fundamental groups
Abstract
We survey some recent progress in the study of algebraic varieties X with log terminal singularities, especially, the uni-ruledness of the smooth locus X^0 of X, the fundamental group of X^0 and the automorphisms group on (smooth or singular) X when dim X = 2. The full automorphism groups of a few interesting types of K3 surfaces are described, mainly by Keum-Kondo. We conjecture that when X is Q-Fano then X^0 has a finite fundamental group, which had been proved if either dim X < 3 or the Fano index is bigger than dim X - 2. We also conjecture that when X is a log Enriques (e.g. a normal K3 or a normal Enriques) surface then either pi_1(X^0) is finite or X has an abelian surface as its quasi-etale cover, which has been proved by Catanese-Keum-Oguiso under some extra conditions.
Cite
@article{arxiv.math/0210005,
title = {Algebraic surfaces with quotient singularities - including some discussion on automorphisms and fundamental groups},
author = {J. Keum and D. -Q. Zhang},
journal= {arXiv preprint arXiv:math/0210005},
year = {2018}
}
Comments
26 pages, Proc. Alg. Geom. in East Asia, Kyoto, 3-10 Aug 2001, A. Ohbuchi et al (eds), to appear