5 problems

Let $V\subset \mathbb{P}^{n}$ be a projective hypersurface with isolated singularities. A hypersurface is homaloidal when its gradient map is birational, equivalently when its pola…

Let $k>2$, let $V\subset\mathbb{P}^{n}$ be a projective hypersurface with only isolated singular points, and let $d=\deg V$. Huh's finiteness conjecture. For sufficiently large $n$…

Let $V\subset \mathbb{P}^{n}$ be a projective hypersurface with only isolated singularities, defined by a homogeneous polynomial $f$ of degree $d$, and let the polar degree of $V$…

Let $k$ be a positive integer. A projective hypersurface is defined by a homogeneous polynomial in a projective space, and it has only isolated singular points when its singular lo…

Let $V(h)\subseteq\mathbb{P}^n$ be a projective hypersurface defined by a homogeneous polynomial $h$ of degree $d$, with only isolated singular points, and let its polar degree be…