7 problems

Let $P_n(X,\beta)_{\varepsilon}$ and $P_n(X,\beta)_{-\varepsilon}$ be the stable-pair moduli spaces for parameters on the two sides of the wall at $t_0=0$, with $0<\varepsilon\ll1$…

Fix $\sigma=iH$ for an ample divisor $H$, $v=(\beta,n)\in N_{\leq 1}(S)$, and a positive rational wall parameter $t_0\in W\cap\mathbb{Q}_{>0}$. For $t_{\pm}=t_0\pm\varepsilon$ with…

Let $I_n(X,\beta)$ and $P_n(X,\beta)$ be the MNOP and stable-pair moduli spaces, respectively, and let $\mathcal{DT}^{\mathbb{C}^{\ast}}(-)$ denote their $\mathbb{C}^{\ast}$-equiva…

Let $X$ be the local Calabi–Yau threefold associated with the surface $S$, let $v=(\beta,n)\in N_{\leq 1}(S)$, and let $\sigma_1=B_1+iH_1$ and $\sigma_2=B_2+iH_2$ be stability cond…

Let $\mathfrak{M}$ be a quasi-smooth QCA derived stack, let $\mathcal{N}=t_0(\Omega_{\mathfrak{M}}[-1])$ be its associated d-critical locus, and let $\mathcal{N}_{\mathrm{st}}$ be…

Fix $(\beta,n)$ and choose stability parameters $t_1>t_2>\cdots>t_N>0$ away from the finitely many walls. Let $I_n(X,\beta)$ be the MNOP moduli space, $P_n(X,\beta)$ the stable-pai…

Let $M_{X,\sigma}$ be the moduli space under consideration, let $\mathcal{DT}^{\mathbb{C}^{\ast}}(M_{X,\sigma})$ be its $\mathbb{C}^{\ast}$-equivariant categorical DT theory, and l…