8 problems

Let $X$ be a manifold with a simple normal crossings divisor $\Delta_1=\sum Y_i$, let $L$ be the relevant coefficient bundle, and let $C^\infty_K(X,\Delta_1,L)$ be the space of smo…

Let $M$ be a complex manifold and let $D$ be a reduced free divisor of $M$. An irreducible subvariety $Z$ is weakly log transverse to $D$ when it satisfies the paper's weak log tra…

Let $M$ be a complex manifold and let $D$ be a reduced free divisor of $M$. A constructible function $\gamma$ is weakly log transverse to $D$ when it satisfies the weak log transve…

Let $X$ be a proper normal crossings surface with graph-like singular locus described by a trivalent graph $G(X)$ and orientable dual intersection complex. For each edge $e$ whose…

Let $X$ be a normal crossings surface with graph-like singular locus and orientable dual intersection complex, arising as the zero locus of a section $s$ of a line bundle $L$ on a…

Faber's conjecture. A free divisor has only normal crossing singularities if and only if it is normal crossing in codimension $1$.

Consider a completely integrable Pfaffian system with normal crossings whose two monomial exponents are $(p,q)$ and $(p',q')$, and let $A_{0,0}$ and $B_{0,0}$ denote the matrices o…

Let $(\Sigma_0,\Delta_0,\xi_0)$ be a coordinated normal crossing scheme over $k$, and let $\Phi_0$ be any effective divisor of $\Sigma_0$. A weakly admissible composition of blowin…