Smoothness conjecture for Fano schemes of bounded-rank symmetric matrices
Let Fk(SDnr)\mathrm{\textbf{F}}_{k}(\mathrm{SD}_n^r)Fk(SDnr) denote the Fano scheme of kkk-planes contained in the space of symmetric n×nn\times nn×n matrices of rank at most rrr. Let κ(s)\kappa(s)κ(s) be…