The fibrewise Hermitian Yang–Mills conjecture for the universal connection

Let $\mathfrak{p}_\zeta:\mathbb{P}\to\mathbb{M}$ be the universal bundle with connection $\mathbb{A}$, and let $p_\zeta:P_\zeta\to M_\zeta$ denote its restriction to a fibre. The fibrewise Hermitian Yang–Mills conjecture. The connection $\mathbb{A}$ restricts to fibrewise Hermitian Yang–Mills connections on $p_\zeta:P_\zeta\to M_\zeta$, asymptotic at rate $1-m$ to the flat connection; furthermore, this connection is irreducible and unobstructed. The conjecture is conditional in the source on the preceding Calabi–Yau ALE conjecture, and its resolution is not established there.