On the graded resolution of ideals of a few general fat points of \(\mathbb P^n\)
Let \(I\) be the ideal of \(r+1<n+1\) general fat points of \(\mathbb P^n\) with multiplicities \((a,b,\ldots,b),\) where \(a\geq 2b.\) The graded Betti numbers of \(I\) are explicitly computed. The hypotheses permit to say that \(I\) is projectively equivalent to a monomial splittable ideal [the notion of splittable ideal was introduced by \textit{S. Eliahou} and \textit{M. Kervaire}, J. Algebra 129, 1--25 (1990; Zbl 0701.13006)]. So a sequence of splittings of \(I\) is performed, using ideals whose graded Betti numbers can easily be computed. Finally the graded Betti numbers of \(I\) are recovered from those of such ideals.
scientific article; zbMATH DE number 2173216