Non-finiteness properties of fundamental groups of smooth projective varieties

Details Non-finiteness properties of fundamental groups of smooth projective varieties Non-finiteness properties of fundamental groups of smooth projective varieties

2006-09-15

arxiv.org/abs/math/0609456v3

Journal f\"ur die reine und angewandte Mathematik 629 (2009), 89-105

Mathematics

Algebraic Geometry

16 pages

Scientific paper

10.1515/crelle.2009.027

For each integer n\ge 2, 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 Z\pi_1(M), is free of infinite rank. As a result, we give a negative answer to a question of Koll'ar 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.

Affiliated with

Also associated with

No associations

Rating

Non-finiteness properties of fundamental groups of smooth projective varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Non-finiteness properties of fundamental groups of smooth projective varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Non-finiteness properties of fundamental groups of smooth projective varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-282905