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

✍ Scribed by J. Keum; D.-Q. Zhang

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 224 KB
• Volume: 170
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(01)00110-4

✦ Synopsis

We investigate when the fundamental group of the smooth part of a K3 surface or Enriques surface with Du Val singularities, is ÿnite. As a corollary we give an e ective 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 Kollar et al. (J. Algebra Geom. 1 (1992) 429) which is still open when the dimension is at least 4) would imply that every log terminal Fano variety has a ÿnite fundamental group.