6 problems

Let $R=\mathbb Z[u,v,w,x,y,z]$, let ${\mathfrak a}$ be generated by the size-two minors of … so ${\mathfrak a}=(\Delta_1,\Delta_2,\Delta_3)R$ with $\Delta_1=vz-wy$,…

Let $0\leq f<g$, let ${\cal M}_g$ be the moduli space of smooth curves of genus $g$, and let ${\cal H}_g$ be the hyperelliptic locus when $p\geq3$. Write $V_{g,f}$ for the locus of…

Let $k$ be an algebraically closed field of characteristic $p$, and let ${\cal M}_g$ be the moduli space of smooth curves of genus $g$. For a curve $X$ of genus $g$, write $J_X$ fo…

Singh's conjecture. There exists $k\in\mathbb N$ such that

Let $p$ be a prime number such that $p \neq 3$. The quantity $\mu_p(\mathcal{F}^{+}(Y))$ denotes the average size of the $p$-torsion subgroup in the class groups of the positive-di…

CohenLenstra conjecture. For every $A\in S$,