Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

I would like to know if there is an explicit example of a finitely presented group that can not be realised as the (topological) fundamental group of a normal complex quasi-projective variety?

share|improve this question
add comment

1 Answer

up vote 8 down vote accepted

Yes, sure. Take any polycyclic group which is not virtually nilpotent (e.g. upper triangular matrices with entries in $GL_n(\mathbb{Z})$, $n\ge 2$). This cannot be the fundamental group of a normal quasiprojective variety by a theorem of Nori and myself [Solvable fundamental groups of algebraic varieties..., Composito 1999]. There are many other sorts of examples.

share|improve this answer
    
Dear Donu, thank you very much for this quick answer! –  aglearner Jun 13 '13 at 15:28
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.