6 problems

Homaloidal polynomial degree conjecture. If $n>2$ and $d>2$, then

Prehomogeneous-space conjecture. Any homaloidal EKP-polynomial is a relative invariant of a regular prehomogeneous space.

Let $G$ be an undirected graph, and let $P_G$ denote the spanning tree generating function corresponding to $G$. A polynomial is homaloidal if its polar map is birational. Chordali…

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…

Dolgachev's conjecture. A homaloidal polynomial whose multiplicative Legendre transform is a polynomial must be a relative invariant of a regular prehomogeneous vector space.

Let $F\in\mathbb C[x_0,x_1,x_2]$ be a homogeneous polynomial, let $V(F)\subset\mathbb P^2$ be its zero locus, and let … be its polar transformation. A polynomial is homaloidal when…