7 problems

It is a long-standing question to determine the lower bound for the slopes of effective divisors in $\overline{\mathcal M}_g$. Harris–Morrison's slope conjecture. The Brill–Noether…

Let $(F,g)$ be a polarized irreducible holomorphic symplectic fourfold deformation equivalent to the Hilbert scheme of length-two subschemes of a K3 surface. Let…

Let $D$ be an effective divisor on $\overline{\mathcal{M}}_g$, with slope $s(D)$ defined from its class in the standard basis of the Picard group. Harris–Morrison's equality conjec…

Let $\overline{\mathcal{M}}_g$ be the moduli space of stable curves of genus $g$, and let $s_g$ be its slope. For an effective divisor $D$ on $\overline{\mathcal{M}}_g$, write … wh…

Conjectural formula for $C_{\lambda}^{\mathcal{T}}$. In the thesis cited by the authors, it was conjectured that

Let $g\geq 1$, let $n$ be a positive integer, and let $r_1,\ldots,r_n$ be nonnegative integers satisfying … For the moduli spaces $\overline{M}_{g,n}$, write $\psi_i$ for the cotan…

Let $\overline{\mathcal M}_{g}$ be the Deligne–Mumford moduli space of genus $g$ stable curves. For an effective divisor $D=a\lambda-\sum_{i=0}^{\lfloor g/2\rfloor}b_i\delta_i$ wit…