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Algebraic surfaces with quotient singularities - including some discussion on automorphisms and fundamental groups | | J. Keum
; D. -Q. Zhang
; | | Date: |
1 Oct 2002 | | Subject: | Algebraic Geometry MSC-class: 14J17; 14J50; 14F35 | math.AG | | 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. | | Source: | arXiv, math.AG/0210005 | | Services: | Forum | Review | PDF | Favorites | |
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