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I have several questions on Hilbert scheme of Gushel-Mukai varieties. Let $X$ be a Gushel-Mukai fourfold and let $\mathcal{H}_3$ be Hilbert scheme of twisted cubics. I was wondering what is the ...

Let $X$ be a smooth Gushel-Mukai threefold, there are following four cases: $X_1$ is a special Gushel-Mukai with branch locus $\mathcal{B}$ on $Y_5$ general, i.e, it does contain any line or conic. $\...