3-dimensional sundials

Enrico Carlini; Maria Catalisano; Anthony Geramita

Open Mathematics (2011)

  • Volume: 9, Issue: 5, page 949-971
  • ISSN: 2391-5455

Abstract

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R. Hartshorne and A. Hirschowitz proved that a generic collection of lines on ℙn, n≥3, has bipolynomial Hilbert function. We extend this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., a union of schemes obtained by degenerating pairs of skew lines).

How to cite

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Enrico Carlini, Maria Catalisano, and Anthony Geramita. "3-dimensional sundials." Open Mathematics 9.5 (2011): 949-971. <http://eudml.org/doc/269063>.

@article{EnricoCarlini2011,
abstract = {R. Hartshorne and A. Hirschowitz proved that a generic collection of lines on ℙn, n≥3, has bipolynomial Hilbert function. We extend this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., a union of schemes obtained by degenerating pairs of skew lines).},
author = {Enrico Carlini, Maria Catalisano, Anthony Geramita},
journal = {Open Mathematics},
keywords = {Hilbert functions; Subspace arrangements; Configuration of linear spaces; Degenerations; Castelnuovo’s sequence; Specializations; subspace arrangements; subspace arrangements; configuration of linear spaces; degenerations; Castelnuovo's sequence; specializations},
language = {eng},
number = {5},
pages = {949-971},
title = {3-dimensional sundials},
url = {http://eudml.org/doc/269063},
volume = {9},
year = {2011},
}

TY - JOUR
AU - Enrico Carlini
AU - Maria Catalisano
AU - Anthony Geramita
TI - 3-dimensional sundials
JO - Open Mathematics
PY - 2011
VL - 9
IS - 5
SP - 949
EP - 971
AB - R. Hartshorne and A. Hirschowitz proved that a generic collection of lines on ℙn, n≥3, has bipolynomial Hilbert function. We extend this result to a specialization of the collection of generic lines, by considering a union of lines and 3-dimensional sundials (i.e., a union of schemes obtained by degenerating pairs of skew lines).
LA - eng
KW - Hilbert functions; Subspace arrangements; Configuration of linear spaces; Degenerations; Castelnuovo’s sequence; Specializations; subspace arrangements; subspace arrangements; configuration of linear spaces; degenerations; Castelnuovo's sequence; specializations
UR - http://eudml.org/doc/269063
ER -

References

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  14. [14] CoCoA: a system for making Computations in Commutative Algebra, available at http://cocoa.dima.unige.it 
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