Conductor and separating degrees for sets of points in $\mathbb{P}^r$ and in $\mathbb{P}^1 \times \mathbb{P}^1$

Marino, Lucia

Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 2, pp. 397-421

Résumé

We attempt to generalize conductor degree's results, known in $\mathbb{P}^2$, to the case of 0-dimensional schemes of $\mathbb{P}^r$. In the first part of this paper, we consider the problem of characterizing the sequences generators's degrees of the conductor which are compatible with a fixed postulation (or Hilbert function) for a set of points in $\mathbb{P}^r$ and we determine the conductor degree of every point in a $r$-partial intersection. In addition, we define the separating degree of a point for a 0-dimensional subscheme of a smooth quadric $Q = \mathbb{P}^1 \times \mathbb{P}^1$ and we give some results in case of special subschemes.