Segments and Hilbert schemes of points |
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Authors: | Francesca Cioffi Paolo Lella Maria Grazia Marinari Margherita Roggero |
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Institution: | aUniversità degli Studi di Napoli, Dipartimento di Matematica e Applicazioni, Complesso univ. di Monte S. Angelo, Via Cintia, 80126 Napoli, Italy;bUniversità degli Studi di Torino, Dipartimento di Matematica, Via Carlo Alberto 10, 10123 Torino, Italy;cUniversità degli Studi di Genova, Dipartimento di Matematica, Via Dodecaneso 35, 16146 Genova, Italy |
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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 (as, for example, the degrevlex order) in the Hilbert scheme of points in Pn. 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. |
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Keywords: | Borel ideal Segment ideal Hilbert scheme of points Gotzmann number Grö bner stratum Degrevlex term order |
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