1
vote
0answers
214 views

lifts of maps to $\mathcal{M}_{1,1}$

Hi, here's there's a construction about elliptic curves that I do not completely understand. Suppose I consider the two following families of elliptic curves over $\mathbb{C}^*$. The first, which I ...
3
votes
2answers
258 views

Analogue of Shafarevich-Ogg's theorem over complex numbers

Let $f:E\to D^*$ be a family of complex elliptic curves parametrized by the punctured open disk $D^*.$ Assume that the monodromy on $H^1$ is trivial (i.e. $R^1f_*\mathbb Z$ is a constant sheaf on ...