3 problems

Let $Q$ be a base scheme, let $W$ be a finite-dimensional vector space with homogeneous coordinate algebra … and let ${\mathcal{I}}\subset{}_{Q}{\mathcal{S}}$ be a linear ideal she…

Let $X\subset \mathbb P^r$ be a $k$-smooth, irreducible, non-degenerate variety of dimension $n$, and let $f(r,n,k)$ be the function in the extended Hartshorne conjecture. Bold for…

There is a suitable function $f(r,n,k)$. Let $X\subset \mathbb P^r$ be a $k$-smooth, irreducible, non-degenerate variety of dimension $n$. Extended Hartshorne's conjecture. If…