3-dimensional sundials

• Autorzy: Enrico Carlini , Maria Catalisano , Anthony Geramita
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

Hilbert functions; Subspace arrangements; Configuration of linear spaces; Degenerations; Castelnuovo’s sequence; Specializations

Kategorie tematyczne

• 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincar\'e series
• 14N20: Configurations and arrangements of linear subspaces

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 5
• Strony: 949-971

Daty

wydano

2011-10-01

online

2011-07-26

Twórcy

autor

Enrico Carlini

• Politecnico di Torino

autor

Maria Catalisano

• Università di Genova

autor

Anthony Geramita

Bibliografia

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• [5] Carlini E., Catalisano M.V., Geramita A.V., Reduced and non-reduced linear spaces: lines and points (in preparation)
• [6] Carlini E., Chiantini L., Geramita A.V., Complete intersections on general hypersurfaces. Michigan Math. J., 2008, 57, 121–136 http://dx.doi.org/10.1307/mmj/1220879400
• [7] Catalisano M.V., Geramita A.V., Gimigliano A., Ranks of tensors, secant varieties of Segre varieties and fat points, Linear Algebra Appl., 2002, 355, 263–285 http://dx.doi.org/10.1016/S0024-3795(02)00352-X
• [8] Catalisano M.V., Geramita A.V., Gimigliano A., Erratum to: “Ranks of tensors, secant varieties of Segre varieties and fat points” [Linear Algebra Appl. 355 (2002) 263–285], Linear Algebra Appl., 2003, 367, 347–348 http://dx.doi.org/10.1016/S0024-3795(03)00455-5
• [9] Catalisano M.V., Geramita A.V., Gimigliano A., Higher secant varieties of Segre-Veronese varieties, In: Projective Varieties with Unexpected Properties, Walter de Gruyter, Berlin, 2005, 81–107
• [10] Catalisano M.V., Geramita A.V., Gimigliano A., Secant varieties of Grassmann varieties, Proc. Amer. Math. Soc., 2005, 133(3), 633–642 http://dx.doi.org/10.1090/S0002-9939-04-07632-4
• [11] Catalisano M.V., Geramita A.V., Gimigliano A., Segre-Veronese embeddings of ℙ1×ℙ1×ℙ1 and their secant varieties, Collect. Math., 2007, 58(1), 1–24
• [12] Catalisano M.V., Geramita A.V., Gimigliano A., Secant varieties of ℙ1 ×…×ℙ1 (n-times) are not defective for n ≥ 5, J. Algebraic Geom., 2011, 20(2), 295–327
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Identyfikatory

DOI

10.2478/s11533-011-0054-7