On subschemes of \(0\)-dimensional schemes with given graded Betti numbers (Q412534)

The following review uses the abstract of the paper:NEWLINENEWLINEIn the paper under review, the authors study the subschemes of a \(0\)-dimensional scheme \(X\) for which the Hilbert function are known. More precisely, The authors find which kind of subscheme can not stay in \(X\) and in the codimension \(2\) case what subschemes must be in \(X\). In addition, the authors study the subschemes of a \(0\)-dimensional scheme \(X\) for which the graded Betti numbers are known. More precisely, the authors study the case of \(2\)-codimensional partial intersection schemes or Artinian monomial ideals. The authors give complete results for almost complete intersections and other suitable Betti sequences.