8 problems

Ciliberto–van der Geer's conjecture. If $1\le \ell\le g-3$, then

Let $(B,\Xi)$ be a simple principally polarized abelian variety of dimension $g$, and suppose that $(B,\Xi)\notin N_{g,i}$ for every $i\geq k\geq1$. Here $N_k(B,\Xi)\subset B$ is t…

Let $g$ and $k$ be integers with $1\leq k\leq g-3$, and let $N$ be an irreducible component of the Andreotti–Mayer locus $N_{g,k}$ whose general point corresponds to a principally…

Folk conjecture on Andreotti–Mayer loci. 1. All irreducible components of $N_{g-4}$ except the locus of Jacobians ${\mathcal J}_g$ are contained in the theta-null divisor…

Let ${\mathcal A}_g$ be the moduli space of principally polarized abelian varieties of dimension $g$, and let … A principally polarized abelian variety is simple if it is not isoge…

Let ${\mathcal A}_g$ be the moduli space of principally polarized abelian varieties of dimension $g$, and let … The hyperelliptic locus is the locus of principally polarized abelia…

Let ${\mathcal A}_g$ denote the moduli space of principally polarized abelian varieties of dimension $g$, and let … A principally polarized abelian variety is decomposable if it is…

Let ${\mathcal A}_g$ be the moduli space of principally polarized abelian varieties, and let $G_k$ denote the loci introduced in the paper in analogy with the Andreotti–Mayer loci.…