5 problems

Let $\mathcal{M}_{g,P}$ be the moduli space of smooth genus-$g$ curves with marked points $P$, and let $W_{m_*,P}$ denote the combinatorial class associated with ribbon graphs havi…

Let $Q=\mathbb{Q}[a_1,\dots,a_n]$, and let $\Omega^m_{g,n}\in R^*({\overline{\mathcal{M}}}_{g,n+m})\otimes_{\mathbb{Q}}Q$ be the class obtained by summing the tree contributions de…

Let $M_{d,\chi}$ be the moduli space under consideration, and let the tautological generators in $A^*(M_{d,\chi})$ be those defined in. A relation among these generators has degree…

Let $C$ be an irreducible nonsingular projective curve of genus $g\geq 2$, let ${\mathcal M}_{\mathrm{Dol}}$ be its twisted Dolbeault moduli space with Hitchin fibration $h$, and l…

Let $(a_1,\ldots,a_n)$ be a partition of $2g-2$ with non-negative parts. For sufficiently large $r$, let $\mathcal{W}_{g; a_1, \dots, a_n}(r)=r^{g-1}W^r_{g,n}(a_1, \dots, a_n)$ be…