Fundamental groups of moduli stacks of smooth Weierstrass fibrations

Details Fundamental groups of moduli stacks of smooth Weierstrass fibrations Fundamental groups of moduli stacks of smooth Weierstrass fibrations

2007-12-20

arxiv.org/abs/0712.3374v1

Mathematics

Algebraic Geometry

38 pages

Scientific paper

We give finite presentations for the fundamental group of moduli stacks of smooth Weierstrass curves over complex projective space P^n which extend the classical result for elliptic curves to positive dimensional base. We thus get natural generalisations of SL_2(Z) and pave the way to understanding the fundamental group of moduli stacks of elliptic surfaces in general. Our approach exploits the natural involution on Weierstrass curves and the identification of its fixed loci with smooth hypersurfaces in an appropriate linear system on a projective line bundle over P^n. The fundamental group of the corresponding discriminant complement can be presented in terms of finitely many generators and relations using methods in the Zariski tradition, which were sucessfully elaborated in mathAG/0602371.

Affiliated with

Also associated with

No associations

Rating

Fundamental groups of moduli stacks of smooth Weierstrass fibrations 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 Fundamental groups of moduli stacks of smooth Weierstrass fibrations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fundamental groups of moduli stacks of smooth Weierstrass fibrations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-2872