Using results obtained from a study of homogeneous ideals sharing the same initial ideal with respect to some term order, we prove the singularity of the point corresponding to a segment ideal with respect to a degreverse term order in the Hilbert scheme of points in P^n. In this context, we look into the properties of several types of "segment" ideals that we define and compare. This study also leads us to focus on the connections between the shape of generators of Borel ideals and the related Hilbert polynomial, thus providing an algorithm for computing all saturated Borel ideals with a given Hilbert polynomial.

Segments and Hilbert schemes of points.

LELLA, PAOLO;ROGGERO, Margherita
2011-01-01

Abstract

Using results obtained from a study of homogeneous ideals sharing the same initial ideal with respect to some term order, we prove the singularity of the point corresponding to a segment ideal with respect to a degreverse term order in the Hilbert scheme of points in P^n. In this context, we look into the properties of several types of "segment" ideals that we define and compare. This study also leads us to focus on the connections between the shape of generators of Borel ideals and the related Hilbert polynomial, thus providing an algorithm for computing all saturated Borel ideals with a given Hilbert polynomial.
2011
311
2238
2252
http://arxiv.org/abs/1003.2951
Hilbert scheme; term ordering.
Francesca Cioffi; Paolo Lella; Maria Grazia Marinari; Margherita Roggero
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/83239
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