4 problems

Douglas's conjecture. Conjecture A holds true, and its induced extension class $\tau_I$ is identified with the fundamental class of $X_I$, namely the extension class induced by the…

Let $I \subset \mathbb{C}[z_1,\ldots,z_d]$ be a homogeneous ideal of infinite co-dimension, let … and set $I^\bot=H^2_d\ominus I$. Define $S^I=(S_1,\ldots,S_d)$ on $I^\bot$ by … Th…

Clouâtre–Davidson's conjecture. Conversely, every $\cA_d$-Henkin measure is also a classical Henkin measure; equivalently, the two notions agree.

Let $\mathrm{A}(\mathbb{B}_d)$ be the ball algebra on the unit ball $\mathbb{B}_d$, let $\mathcal{A}_d$ be the norm-closed polynomial multiplier algebra of the Drury–Arveson space,…