All Questions

I'm trying to construct complete smooth curves $C$ in $\overline{M}_g$ such that for all points $S \in C \cap \mathcal{M}_g$, its Jacobian $\text{Jac}(S)$ satisfies $\text{End}(\text{Jac}(S)) = \...

Let $M_{3,1}$ be the (coarse, non-compactified) moduli space of genus $3$ curves with a marked point over a field $k$ of characteristic zero. Throwing away the hyperelliptic curves, take the open ...

Consider the moduli space $\mathcal{A}_{g,n}$ of abelian varieties with some level $n \geq 3$ structure. For simplicity, we just denote it by $\mathcal{A}_{g}$ and drop $n$. Denote the locus of ...

Let $Y$ be an integral curve whose only singularity is one simple node at a point $y$, and $\pi:X\rightarrow Y$ be the normalization with $\pi^{-1}(y)=\{x,z\}$. $J(X)$ is the Jacobian of $X$, and $\...