7 problems

Let $L$ be the hypersurface arrangement under consideration. Write … Here $\Omega^\bullet(\log L)$ is the logarithmic de Rham complex associated with $L$, and $i_2$ is the inclusio…

Mustăță–Popa's logarithmic-form conjecture. If

Let ${\mathcal{A}}$ be a hyperplane arrangement, let $H\in{\mathcal{A}}$, and write ${\mathcal{A}}'$ for the deletion and ${\mathcal{A}}^H$ for the restriction to $H$. Let … be the…

Let ${\mathcal{A}}$ be a hyperplane arrangement, and for an integer $k$ call it $k$-critical when … and … for every $H\in{\mathcal{A}}$. Here $|{\mathcal{A}}|$ denotes the number o…

Let ${\mathcal{A}}'$ be an essential and free arrangement in $V={\mathbb{K}}^\ell$ with $\ell\geq 4$. Let $X$ be a generic subspace with $\dim X>2$, and define the restriction … He…

Let $f=f_1\cdots f_d\in R=\mathbb{C}[x_1,\dots,x_n]$ define a reduced hyperplane arrangement $\mathscr{A}$ in $X=\mathbb{C}^n$, and let $U=X\setminus\mathscr{A}$. Write…

Let $Z$ be a reduced closed subscheme of a smooth variety $X$ of dimension $n$, let $f:Y\to X$ be a log resolution, and let $E$ be the reduced exceptional divisor over $Z$. Depth–v…