3 problems

Let $g\in\mathbb C[x_1,\ldots,x_n]$ be a polynomial of degree $d$ whose reduced zero locus is a central, essential, indecomposable hyperplane arrangement. The $n/d$-conjecture. The…

Let $f: X \longrightarrow \mathbb{C}$ be a non-constant regular function and let $x \in X$. Denote by $Z_{\textnormal{mot}, x}(f; s)$ the local motivic zeta function and by…

Let $\mathcal I=(f_1,\ldots,f_r)$ be an ideal in $\mathbb C[x_0,\ldots,x_n]$ whose associated subscheme $Y=V(\mathcal I)$ in $\mathbb C^{n+1}$ contains the origin. Let…