Grzegorz Malara

From Demailly's Inequality to Harbourne--Huneke Containments for General Points

Let $I$ be the defining ideal of a general set of $s$ points in projective $N$-space over an algebraically closed field. Harbourne and Huneke conjectured the strengthened symbolic containment $$ I^{(Nr)}\subseteq \mathfrak{m}^{r(N-1)}I^r $$ for every $r\ge 1$. For general points this was known in low dimension and for...