5 problems

Let $(M,\omega)$ be a higher-dimensional Kähler manifold, let $\mathcal{E}$ be a reflexive sheaf on $M$, and let $A(t)$ be the Yang–Mills flow associated with $\mathcal{E}$. Suppos…

Square-integrability conjecture. The curvature of the hyperholomorphic connection has square-integrable curvature.

Let $A$ be an admissible Hermitian–Yang–Mills connection on $(\mathcal{E},B)$, and let $\hat{\mathcal{E}}$ be any chosen optimal extension of $\mathcal{E}$ at $0$. An analytic tang…

Let $B$ be a ball in $\mathbb C^n$ and let $\mathcal E$ be a reflexive sheaf over $B$ with an isolated singularity at $0$. For an admissible Hermitian–Yang–Mills connection $A$ on…

Generic smoothness conjecture. If $\operatorname{diam} M=2$, the corresponding component of ${\rm M}_{\mathbb P^3}(c_1,c_2,c_3)$ is generically smooth.