Conductor and separating degrees for sets of points in r and in 1 × 1

Lucia Marino

Bollettino dell'Unione Matematica Italiana (2006)

  • Volume: 9-B, Issue: 2, page 397-421
  • ISSN: 0392-4033

Abstract

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We attempt to generalize conductor degree's results, known in 2 , to the case of 0-dimensional schemes of 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 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 = 1 × 1 and we give some results in case of special subschemes.

How to cite

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Marino, 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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  1. ABRESCIA, S. - BAZZOTTI, L. - MARINO, L., Conductor Degree and Socle Degree, Le Matematiche, vol LVI- Fasc. I (2001), 129-148. 
  2. BAZZOTTI, L., Doctoral Thesis, Florence, 2003. 
  3. GERAMITA, A. V. - KREUZER, M. - ROBBIANO, L., Cayley-Bacharach Schemes and their canonical modules, Transactions of the American Mathematical Society, vol 339 (1) (1993), 163-189. Zbl0793.14002
  4. GERAMITA, A. V. - MAROSCIA, P. - ROBERTS, L. G., The Hilbert function of a reduced k-algebra, J. Lond. Math. Soc. (2), 28 (1983), 443-452. Zbl0535.13012
  5. GIUFFRIDA, S. - MAGGIONI, R. - RAGUSA, A., On the postulation of 0-dimensional subschemes on a smooth quadric, Pacific J. of Mathematics, 155 (1992), 251-282. Zbl0723.14035
  6. GERAMITA, A.V. - TADAHITO, H. - YONG SU, S., An alternative to the Hilbert Function for the Ideal of a Finite Set of Points in n , to appear: Illinois Journ. of Math (28 pages). Zbl0943.13012
  7. MAGGIONI, R. - RAGUSA, A., A classification of arithmetically Cohen Macaulay varieties with given Hilbert Function, unpublished. Zbl0616.14026
  8. MIGLIORE, J. C., Introduction to Liaison Theory and Deficiency Modules, Birkhäuser, 1998. Zbl0921.14033
  9. ORECCHIA, F., Points in generic positon and conductors of curves with ordinary singularities, J. Lond. Math. Soc. (2), 24 (1981), 85-96. Zbl0492.14017
  10. PEEVA, I., Personal communications. 
  11. RAGUSA, A. - ZAPPALA, G., Partial intersection and graded Betti numbers, to appear on Beiträge zur Algebra und Geometrie. Zbl1033.13004
  12. SABOURIN, L., N-type vectors and the Cayley-Bacharach property, Comm. in Alg.30 (8) (2002), 3891-3915. Zbl1095.13526

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