5 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 $F$ be an $N$-variable homaloidal polynomial of degree $r$, and put $H=\mathcal{ML}(F)$. Let $b^{[0]}(s)$ denote a $b$-function for the pair $(F,H)$. For each $k$, let…

Let $F_k^{(r)}$ be the $k$-times polarization of the size-$r$ sub-Hankel determinant $P_1$, and let $H_k$ be its multiplicative Legendre transform. Conjecture B. The corresponding…

Let $P_1$, $P_2$, $Q_1$, and $Q_2$ be the relative invariants defined in the previous section. Put … and let $K=\phi_{(r-1,1)}=P_1^{r-1}P_2^{-r^2+2r}$. Conjecture A. The following…

Let $b(\underline{s})$ be a several-variable $b$-function of semi-invariants on a more general prehomogeneous vector space, and suppose it has the form … where $d_i\in\mathbb{N}$,…