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

Bollettino dell'Unione Matematica Italiana (2006)

- Volume: 9-B, Issue: 2, page 397-421
- ISSN: 0392-4041

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topMarino, Lucia. "Conductor and separating degrees for sets of points in $\mathbb{P}^r$ and in $\mathbb{P}^1 \times \mathbb{P}^1$." Bollettino dell'Unione Matematica Italiana 9-B.2 (2006): 397-421. <http://eudml.org/doc/289635>.

@article{Marino2006,

abstract = {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.},

author = {Marino, Lucia},

journal = {Bollettino dell'Unione Matematica Italiana},

language = {eng},

month = {6},

number = {2},

pages = {397-421},

publisher = {Unione Matematica Italiana},

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

url = {http://eudml.org/doc/289635},

volume = {9-B},

year = {2006},

}

TY - JOUR

AU - Marino, Lucia

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

JO - Bollettino dell'Unione Matematica Italiana

DA - 2006/6//

PB - Unione Matematica Italiana

VL - 9-B

IS - 2

SP - 397

EP - 421

AB - 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.

LA - eng

UR - http://eudml.org/doc/289635

ER -

## References

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- MAGGIONI, R. - RAGUSA, A., A classification of arithmetically Cohen Macaulay varieties with given Hilbert Function, unpublished. Zbl0616.14026
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- ORECCHIA, F., Points in generic positon and conductors of curves with ordinary singularities, J. Lond. Math. Soc. (2), 24 (1981), 85-96. Zbl0492.14017
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- RAGUSA, A. - ZAPPALA, G., Partial intersection and graded Betti numbers, to appear on Beiträge zur Algebra und Geometrie. Zbl1033.13004
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