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

Marino, Lucia

Geodesic

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Conductor and separating degrees for sets of points in

P^{r}

and in

P^{1} \times P^{1}

Marino, Lucia

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

Voir la notice de l'article dans Biblioteca Digitale Italiana di Matematica

Abstract
Résumé

We attempt to generalize conductor degree's results, known in

P^{2}

, to the case of 0-dimensional schemes of

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

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 = P^{1} \times P^{1}

and we give some results in case of special subschemes.

In questo lavoro generalizziamo alcuni risultati sui gradi del conduttore, noti in

P^{2}

, al caso di schemi 0-dimensionali di

P^{r}

. Nella prima parte consideriamo il problema di caratterizzare la sequenza dei gradi dei generatori del conduttore in accordo con una fissata funzione di Hilbert per un insieme di punti in

P^{r}

e determiniamo il grado del conduttore di ogni punto in una

r

-parziale intersezione. Inoltre diamo la definizione di separating degree di un punto per uno schema 0dimensionale su una quadrica liscia

Q = P^{1} \times P^{1}

e proviamo dei risultati per esso nel caso di sottoschemi speciali.

MR Zbl

@article{BUMI_2006_8_9B_2_a8,
     author = {Marino, Lucia},
     title = {Conductor and separating degrees for sets of points in $\mathbb{P}^r$ and in $\mathbb{P}^1 \times \mathbb{P}^1$},
     journal = {Bollettino della Unione matematica italiana},
     pages = {397--421},
     publisher = {mathdoc},
     volume = {Ser. 8, 9B},
     number = {2},
     year = {2006},
     zbl = {1178.13007},
     mrnumber = {2233144},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_2_a8/}
}

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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 della Unione matematica italiana, Série 8, 9B (2006) no. 2, pp. 397-421. https://geodesic-test.mathdoc.fr/item/BUMI_2006_8_9B_2_a8/

Bibliographie
Cité par

[1] S. Abrescia - L. Bazzotti - L. Marino, Conductor Degree and Socle Degree, Le Matematiche, vol LVI- Fasc. I (2001), 129-148.

[2] L. Bazzotti, Doctoral Thesis, Florence, 2003.

[3] A. V. Geramita - M. Kreuzer - L. Robbiano, Cayley-Bacharach Schemes and their canonical modules, Transactions of the American Mathematical Society, vol 339 (1) (1993), 163-189. | Zbl

[4] A. V. Geramita - P. Maroscia - L. G. Roberts, The Hilbert function of a reduced k-algebra, J. Lond. Math. Soc. (2), 28 (1983), 443-452. | Zbl

[5] S. Giuffrida - R. Maggioni - A. Ragusa, On the postulation of 0-dimensional subschemes on a smooth quadric, Pacific J. of Mathematics, 155 (1992), 251-282. | Zbl

[6] A.V. Geramita - H. Tadahito - S. Yong Su, An alternative to the Hilbert Function for the Ideal of a Finite Set of Points in $\mathbb{P}^n$, to appear: Illinois Journ. of Math (28 pages). | Zbl

[7] R. Maggioni - A. Ragusa, A classification of arithmetically Cohen Macaulay varieties with given Hilbert Function, unpublished. | Zbl

[8] J. C. Migliore, Introduction to Liaison Theory and Deficiency Modules, Birkhäuser, 1998. | Zbl

[9] F. Orecchia, Points in generic positon and conductors of curves with ordinary singularities, J. Lond. Math. Soc. (2), 24 (1981), 85-96. | Zbl

[10] I. Peeva, Personal communications.

[11] A. Ragusa - G. Zappala, Partial intersection and graded Betti numbers, to appear on Beiträge zur Algebra und Geometrie. | fulltext EuDML | Zbl

[12] L. Sabourin, N-type vectors and the Cayley-Bacharach property, Comm. in Alg. 30 (8) (2002), 3891-3915. | Zbl