Fundamental groups of moduli stacks of smooth Weierstrass fibrations

@inproceedings{LoenneFundamentalGO,
  title={Fundamental groups of moduli stacks of smooth Weierstrass fibrations},
  author={Michael Loenne}
}
We give finite presentations for the fundamental group of moduli stacks of smooth Weierstrass curves over P n which extend the classical result for ellip-tic curves to positive dimensional base. We thus get natural generalisations of SL 2 Z presented in terms of (1 1 0 1), 1 0 −1 1 and pave the way to understanding the fundamental group of moduli stacks of elliptic surfaces in general. Our approach exploits the natural Z 2-action on Weierstrass curves and the identification of Z 2-fixed loci… CONTINUE READING