6 problems

Vanishing conjecture for Hodge ideals. The vanishing theorem for the Hodge ideals $I_k(D)$ should still hold without the global assumption.

Let $D\subset X=\mathbb{C}^{4n-10}$ be the linear free divisor $D_n$. The Hodge filtration on $\mathcal{O}_X(*D)$ is generated at level $k$ when … for every $l\geq 0$. Generating-l…

Let $X$ be a complex manifold, let $D$ be a divisor satisfying the assumptions of Theorem and Corollary, and let $b_D(s)$ be the relevant Bernstein–Sato polynomial. For a well-filt…

Let $D=\alpha Z$, where $0<\alpha\le 1$ and $Z=(f=0)$ is an integral and reduced effective divisor defined by a weighted homogeneous polynomial $f$ with an isolated singularity at…

Popa's conjecture. The generating-level result for $cO_X(*D)$ should have an analogous formulation for effective $cQ$-divisors in the Hodge-filtration setup considered in the paper…

Hodge ideals and m-adic approximation conjecture. There exists a positive integer $q(r)$ such that, for every such $E$,