9 problems

Smoothness conjecture. The moduli spaces of such stable holomorphic bundles should be smooth.

For an ${\rm SU}(2)$-bundle over ${\mathbb C}\times\Sigma$, consider a finite-energy anti-self-dual instanton, and let ${\mathbb C\mathbb P}^1\times\Sigma$ be the compactification…

Standard-bundle generation conjecture. Every holomorphic bundle on $T_{\theta}$ is a successive extension of standard holomorphic bundles.

Unrestricted-type conjecture. There are no restrictions on the possible types $(\mu_i^+\mid\mu_i^-)$ when both multiplicities are positive, that is, when $\mu_i^{\pm}>0$.

Yau's conjecture. The triple $(X,\Omega,P)$ admits a solution of the Hull–Strominger system.

Let $I\subset\mathbb C^2$ be finite. Write $\mathfrak M_I$ for the stable moduli space of holomorphic bundles associated with $I$, and let … be the bar construction, with its natur…

Let $M$ be a domain in a Stein manifold, let $\hat{M}$ be its envelope of holomorphy, and let $E \to M$ be a holomorphic principal bundle. The extension conjecture. The bundle $E$…

Let ${\mathcal M}^{\rm st}$ be the moduli space of stable bundles on a compact Kähler manifold, and let $\bar{\mathcal M}^{\rm st}$ be a suitable complex-geometric compactification…

Let $X$) be a compact Kähler manifold, let ${\mathcal M}^{\rm st}$ be a moduli space of stable bundles over $X$, and let ${\mathcal E}$ be a generically stable family parameterized…