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

2001/04/02 by JongHae Keum, J. Keum, De‐Qi Zhang +3
Computer Science · Mathematics · #14F35 #14J28 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14F35 #msc:14J28

paper · pdf · doi:10.48550/arxiv.math/0104017

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

arxiv created 2001/04/02 · openalex publication_date 2001/04/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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