Asymptotic of invariants of quasi-projective fundamental groups.

Anatoly LibgoberUniversity of Illinois at Chicago

We discuss distribution of invariants of fundamental groups of smooth quasi-projective varieties with simply connected compactification. One of invariants is the maximal rank of the free quotient and another is the rank of abelianization of the commutator. The discussion will include several boundness results as well as some conjectures.

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