6 problems

Let $V$ be a one-dimensional smooth holomorphic zero variety of an open neighborhood of the closed unit ball $\overline{\mathbb B}$, transversal to the boundary…

Let $V\subset\mathbb{B}^n$ be an affine homogeneous algebraic variety, meaning that there exist finitely many holomorphic homogeneous polynomials $q_1,\ldots,q_m$ such that … Let…

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…

Let $\Omega\subseteq\mathbb{C}^m$ be a bounded strongly pseudoconvex domain with smooth boundary, let $A$ be the algebra of analytic functions under consideration, and let $I$ be a…

Geometric Arveson–Douglas conjecture. The quotient module $Q$ is $p$-essentially normal for every $p>\dim M$.

Let $K$ be a finite dimensional Hilbert space, let $H^2_d$ denote Drury–Arveson space, and let $L\subseteq H^2_d\otimes K$ be a graded submodule. Write $\dim(L)$ for the dimension…