4 problems

The compatibility conjecture. The isomorphism $\eta$ induces an isomorphism of perfect obstruction theories

Let $(\vec{r},n)$ be the discrete parameters for the 4D ADHM quiver, and let $M_{Q_4}(\vec{r},n)$ be its stable representation moduli space. Let $M_{(\mathbb P^1)^4}(\vec{r},n)$ be…

Scheme-theoretic extension conjecture. This bijection can be extended to an isomorphism of schemes, or at least to an isomorphism of the underlying reduced schemes. This would stre…

Let $\mathbb F_p$ be the Hirzebruch surface compactifying the total space $\mathrm{Tot}(\mathcal O_{\mathbb P^1}(-p))$, and consider framed sheaves $(E,\phi_E)$ on $\mathbb F_p$ wi…