8 problems

A generalized multiplicative quiver variety is a variety associated with a quiver and its multiplicative moment-map data; its Poisson structure is the structure induced on the vari…

Irreducibility conjecture. The irreducible component of ${\mathcal{C}_{n,m}}^\circ$ containing ${\mathcal{C}_{n,m}}'$ should be ${\mathcal{C}_{n,m}}^\circ$ itself.

Let $\mathcal{M}_{q,\theta}(Q,\alpha)$ denote a multiplicative quiver variety. A symplectic singularity is a normal singular variety whose smooth locus carries a symplectic form ex…

A multiplicative quiver variety is called a $(2,2)$-case when it is one of the $q$-divisible cases characterized by the relevant $(p(\alpha),n)=(2,2)$ condition. (2,2)-case symplec…

Let $\mathcal{M}_{q,\theta}(Q,\alpha)$ be a multiplicative quiver variety. A symplectic resolution of such a variety should be studied through its local structure, in particular th…

Let $V_{i-1}$ and $V_i$ be the vector spaces associated with adjacent vertices in a bow, and let $A_{i-1}$, $B_{i-1}$, $B'_i$, $a_i$, and $b_{i-1}$ satisfy conditions (i), (a), (S1…

Let $\Gamma$ be a simply-laced supernova graph with monochromatic core, and let $\mathcal{M}^{st}(\Gamma,q,d)$ be the associated stable multiplicative quiver variety, which is a hy…

Let $\mathcal{M}$ be one of the complex surfaces listed as wild Hitchin spaces, and let $\mathcal{M}_n$ be the associated higher Painlevé space of complex dimension $2n$ for…