Families of reduced zero-dimensional schemes.

Migliore, Juan C.. "Families of reduced zero-dimensional schemes.." Collectanea Mathematica 57.2 (2006): 173-192. <http://eudml.org/doc/41835>.

@article{Migliore2006,
abstract = {A great deal of recent activity has centered on the question of whether, for a given Hilbert function, there can fail to be a unique minimum set of graded Betti numbers, and this is closely related to the question of whether the associated Hilbert scheme is irreducible or not. We give a broad class of Hilbert functions for which we show that there is no minimum, and hence that the associated Hilbert sheme is reducible. Furthermore, we show that the Weak Lefschetz Property holds for the general element of one component, while it fails for every element of another component.},
author = {Migliore, Juan C.},
journal = {Collectanea Mathematica},
keywords = {Geometría algebraica; Esquemas; Parametrización; Anillos y módulos de Cohen-Macaulay; postulation Hilbert scheme; graded Betti numbers; linkage},
language = {eng},
number = {2},
pages = {173-192},
title = {Families of reduced zero-dimensional schemes.},
url = {http://eudml.org/doc/41835},
volume = {57},
year = {2006},
}

TY - JOUR
AU - Migliore, Juan C.
TI - Families of reduced zero-dimensional schemes.
JO - Collectanea Mathematica
PY - 2006
VL - 57
IS - 2
SP - 173
EP - 192
AB - A great deal of recent activity has centered on the question of whether, for a given Hilbert function, there can fail to be a unique minimum set of graded Betti numbers, and this is closely related to the question of whether the associated Hilbert scheme is irreducible or not. We give a broad class of Hilbert functions for which we show that there is no minimum, and hence that the associated Hilbert sheme is reducible. Furthermore, we show that the Weak Lefschetz Property holds for the general element of one component, while it fails for every element of another component.
LA - eng
KW - Geometría algebraica; Esquemas; Parametrización; Anillos y módulos de Cohen-Macaulay; postulation Hilbert scheme; graded Betti numbers; linkage
UR - http://eudml.org/doc/41835
ER -