4 problems

Let $n\geq 5$, let $X\subset\mathbb{P}^n$ be a non-singular hypersurface of degree $d\geq 3$, and set … An $m$-plane means a linear projective subspace of dimension $m$ contained i…

Let $\mathrm{\textbf{F}}_{k}(\mathrm{SD}_n^r)$ denote the Fano scheme of $k$-planes contained in the space of symmetric $n\times n$ matrices of rank at most $r$. Let $\kappa(s)$ be…

Let $P_{n,n}^n$ be the permanental hypersurface of $n\times n$ matrices, and let $\mathbf{F}_1(P_{n,n}^n)$ be its Fano scheme of lines. Reduced local-complete-intersection conjectu…

Let $K$ be an algebraically closed field of characteristic zero, let $X^{n-1}\subset \mathbb P^n$ be a hypersurface of degree $n-\lambda$, and let $B\subset \mathbb F(X)$ be an irr…