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

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

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Algebraic Geometry, 14J28; 14F35

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http://salesiana.dossiersoluciones.com/handle/123456789/61208

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0104017
 http://arxiv.org/abs/math/0104017

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arXiv