3 problems

Let $X\subset\mathbb{P}^n$ be a smooth hypersurface of degree $d$, and let $F_1(X)\subset\mathbb{G}(1,n)$ denote the Hilbert scheme of lines contained in $X$. The expected dimensio…

Let $X\subset\mathbb{P}^n$ be a generic union of linear spaces whose components are pairwise non-intersecting. Recall that $X$ has good postulation if, for every degree $d\geq 0$,…

Let $(P,L)$ be a linear space with $d=\#P$, and let $A$ be its associated ring. Set $n$ and $m$ to be the minimum and maximum, respectively, size of a line in $L$. Suppose…