# Arithmetic geometry of the moduli stack of Weierstrass fibrations over $\mathbb{P}^1$

@inproceedings{Park2021ArithmeticGO, title={Arithmetic geometry of the moduli stack of Weierstrass fibrations over \$\mathbb\{P\}^1\$}, author={Jun-yong Park and Johannes Schmitt}, year={2021} }

Coarse moduli spaces of Weierstrass fibrations over the (unparameterized) projective line were constructed by the classical work of [Miranda] using Geometric Invariant Theory. In our paper, we extend this treatment by using results of [Romagny] regarding group actions on stacks to give an explicit construction of the moduli stack Wn of Weierstrass fibrations over an unparameterized P 1 with discriminant degree 12n and a section. We show that it is a smooth algebraic stack and prove that for n… Expand

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