3 problems

Let ${\mathcal A}_4$ be the moduli space of 4-dimensional principally polarized abelian varieties, let $\tau\in{\mathcal A}_4$, and suppose that some theta constant at $\tau$ and i…

Reconstruction conjecture. For every non-hyperelliptic genus $4$ curve over a field of characteristic different from $2$, there exists a two-torsion point

Surjectivity conjecture. The map is surjective when $D$ and $D+v$ range over all effective odd theta characteristic divisors. The conjecture would ensure that the conditional step…