Fundamental groups of open K3 surfaces, Enriques surfaces and Fano 3-folds

Details Fundamental groups of open K3 surfaces, Enriques surfaces and Fano 3-folds Fundamental groups of open K3 surfaces, Enriques surfaces and Fano 3-folds

2001-04-02

arxiv.org/abs/math/0104017v1

Mathematics

Algebraic Geometry

Journal of Pure and Applied Algebra, to appear; 24 pages

Scientific paper

We investigate when the fundamental group of the smooth part of a K3 surface or Enriques surface with Du Val singularities, is finite. As a corollary we give an effective upper bound for the order of the fundamental group of the smooth part of a certain Fano 3-fold. This result supports Conjecture A below, while Conjecture A (or alternatively the rational connectedness conjecture in [KoMiMo] which is still open when the dimension is at least 4) would imply that every log terminal Fano variety has a finite fundamental group (now a Theorem of S. Takayama).

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