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Non-finiteness properties of fundamental groups of smooth projective varieties

Domenii publicaţii > Matematica + Tipuri publicaţii > Articol în revistã ştiinţificã

Autori: A. Dimca, S. Papadima, A.I. Suciu

Editorial: Journal für die reine und angewandte Mathematik, 629, p.89-105, 2009.

Rezumat:

For each integer n > 1, we construct an irreducible, smooth, complex projective variety M of dimension n, whose fundamental group has infinitely generated homology in degree n+1 and whose universal cover is a Stein manifold, homotopy equivalent to an infinite bouquet of n-dimensional spheres. This non-finiteness phenomenon is also reflected in the fact that the homotopy group pi_n(M), viewed as a module over Zpi_1(M), is free of infinite rank. As a result, we give a negative answer to a question of Kollár on the existence of quasi-projective classifying spaces (up to commensurability) for the fundamental groups of smooth projective varieties. To obtain our examples, we develop a complex analog of a method in geometric group theory due to Bestvina and Brady.

Cuvinte cheie: projective group, property FP_n, commensurability, homotopy groups, Stein manifold, irrational pencils, characteristic varieties, complex Morse theory

URL: http://dx.doi.org/10.1515/CRELLE.2009.027