6 problems

Let $X$ be a smooth projective variety, let $\{\gamma_a\}$ and $\{\gamma^a\}$ be dual bases of $H^*(X,\mathbb Q)$, and let $g$ and $k$ be integers with $k>g$. Two-point vanishing c…

Let $X$ be a smooth projective variety. Given a basis $\{\gamma_a\}$ for $H^*(X,\mathbb Q)$, let $x_i,y_i\in H^*(X)$ and let $k\geq 2g-3+r+s$. Using Gathmann's conventions … and ……

For integers $n_i\geq 0$, define $\langle\tau_{n_1,m_1}\dots\tau_{n_s,m_s}\rangle_g$ by … where $c_D(\mathcal{V})$ is Witten's top Chern class and $D=(g-1)/3+\sum_{i=1}^s m_i/3$. L…

Let $\overline{\mathcal M}_{2,2}$ be the moduli space of stable genus-two curves with two markings, let $\overline{\mathcal M}_{2,2}^{(1)}$ be the proposed moduli space of $1$-stab…

Let $H^g_{\alpha,(n)}$ denote the double Hurwitz number in genus $g$ with ramification partitions $\alpha$ and $(n)$, where $\alpha=(\alpha_1,\ldots,\alpha_\ell)$ is a partition of…

Let $\tau_a$ denote the cotangent-line classes used to define intersection numbers on the moduli spaces of stable curves, and let $\boldsymbol{\beth}$ denote the tautological ring…