2 problems

Let $X\subset\mathbb{E}^n$ be an object, and let $X\langle r\rangle$ denote the set of $r$-singular points, where an $r$-singular point is one whose associated fiber has scheme-the…

Let $X \subset \mathbb{P}_{\mathbb{C}}^n$ be a non-degenerate, irreducible projective variety, and let $X^* \subset \mathbb{P}_{\mathbb{C}}^N$ be its projective dual. For…