4 problems

Let $I$ be an ideal of points in $\mathbb{P}^{n-1}$, where $ngeq 2$, and let $I^{(s)}$ denote its $s$-th symbolic power. Write … for the least degree of a nonzero element of $I$. C…

Let $S$ be the homogeneous coordinate ring of $\mathbb{P}^n$, let $Z$ be a general set of $r$ points, and let $I(Z)$ be its vanishing ideal. Let $d$ be the Hilbert regularity of…

Let $S$ be the homogeneous coordinate ring of $\mathbb{P}^n$, let $Z$ be a general set of $r$ points, and let $I_{\langle d\rangle}=\langle I(Z)_d\rangle_S$. For positive integers…

Let $S$ be the homogeneous coordinate ring of $\mathbb{P}^n$, let $Z$ be a general set of $r$ points, and let $I(Z)$ be its vanishing ideal. For an integer $d$ that is the smallest…