# On the Hilbert function of curvilinear zero-dimensional subschemes of projective spaces

E. Ballico; R. Notari; M. Spreafico

Open Mathematics (2003)

- Volume: 1, Issue: 4, page 644-649
- ISSN: 2391-5455

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topE. Ballico, R. Notari, and M. Spreafico. "On the Hilbert function of curvilinear zero-dimensional subschemes of projective spaces." Open Mathematics 1.4 (2003): 644-649. <http://eudml.org/doc/268722>.

@article{E2003,

abstract = {Here we show the existence of strong restrictions for the Hilbert function of zerodimensional curvilinear subschemes of P n with one point as support and with high regularity index.},

author = {E. Ballico, R. Notari, M. Spreafico},

journal = {Open Mathematics},

keywords = {14N05},

language = {eng},

number = {4},

pages = {644-649},

title = {On the Hilbert function of curvilinear zero-dimensional subschemes of projective spaces},

url = {http://eudml.org/doc/268722},

volume = {1},

year = {2003},

}

TY - JOUR

AU - E. Ballico

AU - R. Notari

AU - M. Spreafico

TI - On the Hilbert function of curvilinear zero-dimensional subschemes of projective spaces

JO - Open Mathematics

PY - 2003

VL - 1

IS - 4

SP - 644

EP - 649

AB - Here we show the existence of strong restrictions for the Hilbert function of zerodimensional curvilinear subschemes of P n with one point as support and with high regularity index.

LA - eng

KW - 14N05

UR - http://eudml.org/doc/268722

ER -

## References

top- [1] C. Ciliberto and R. Miranda: “Interpolations on curvilinear schemes”, J. Algebra, Vol. 203, (1998), pp. 677–678. http://dx.doi.org/10.1006/jabr.1997.7241
- [2] Ph. Ellia and Ch. Peskine: “Groupes de points de P 2: caractere et position uniform”, In: Algebraic Geometry, Proceedings, L'Aquila 1988, pp. 111–116, Lect. Notes in Math. 1417, Springer-Verlag, 1990.
- [3] G. Fatabbi and A. Lorenzini: “On a sharp bound for the regularity index of any set of fat points”, J. Pure Appl. Algebra, Vol. 161, (2001), pp. 91–111. http://dx.doi.org/10.1016/S0022-4049(00)00083-9 Zbl0994.14028
- [4] A.V. Geramita, P. Maroscia, L. Roberts: “The Hilbert function of a reduced k-algebra”, J. London Math. Soc., Vol. 28, (1993), pp. 443–452. Zbl0535.13012
- [5] P.V. Thiên: “Segre bound for the regularity index of fat points in P 3”, J. Pure Appl. Alg., Vol. 151, (2000), pp. 197–214. http://dx.doi.org/10.1016/S0022-4049(99)00055-9 Zbl0963.14023

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