Zero-Dimensional Schemes in the Plane - Ballico, E. (Sarajevo Journal of Mathematics, 2024)
Let $Z\subset \mathbb {P}^2$ be a zero-dimensional scheme. Fix $t\in \mathbb {N}$. In this paper we study the following question: find assumptions on $Z$ and $t$ such that $h^1(\mathcal {I}_A(t)) <h^1(\mathcal {I}_Z(t))$ for all $A\subsetneq Z$ and check if $t$ does not exist for a certain class of schemes $Z$. 2010 Mathematics Subject Classification. 14N05.