4 problems

Let $g$ and $d$ be positive integers, and consider the locus of curves $[C]\in \overline{\mathcal{M}}_g$ admitting an admissible cover $f:C\to E$ of degree $d$ to some elliptic cur…

Higher-genus quasimodularity conjecture. The statement of this theorem holds for all $g\ge2$.

Let $g$ be the genus of a smooth curve, and let $d$ denote the degree of a map from that curve to a genus $1$ curve. The resulting $d$-elliptic loci are compactified via admissible…

Let $d>1$ and $n\geq 1$ be integers. Let $W_{d^2}[n]\subset\mathcal M_2$ be the locus of genus-two Riemann surfaces admitting a primitive degree-$d$ elliptic cover with two critica…