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2011 | 9 | 5 | 949-971
Tytuł artykułu

3-dimensional sundials

Treść / Zawartość
Warianty tytułu
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).
Wydawca
Czasopismo
Rocznik
Tom
9
Numer
5
Strony
949-971
Opis fizyczny
Daty
wydano
2011-10-01
online
2011-07-26
Bibliografia
  • [1] Abo H., Ottaviani G., Peterson C., Induction for secant varieties of Segre varieties, Trans. Amer. Math. Soc., 2009, 361(2), 767–792 http://dx.doi.org/10.1090/S0002-9947-08-04725-9
  • [2] Alexander J., Hirschowitz A., Polynomial interpolation in several variables, J. Algebraic Geom., 1995, 4(2), 201–222
  • [3] Bürgisser P., Clausen M., Shokrollahi M.A., Algebraic Complexity Theory, Grundlehren Math. Wiss., 315, Springer, Berlin, 1997
  • [4] Carlini E., Catalisano M.V., Geramita A.V., Bipolynomial Hilbert functions, J. Algebra, 2010, 324(4), 758–781 http://dx.doi.org/10.1016/j.jalgebra.2010.04.008
  • [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
  • [13] Comon P., Mourrain B., Decomposition of quantics in sums of powers of linear forms, Signal Process., 1996, 53(2), 93–107 http://dx.doi.org/10.1016/0165-1684(96)00079-5
  • [14] CoCoA: a system for making Computations in Commutative Algebra, available at http://cocoa.dima.unige.it
  • [15] Hartshorne R., Hirschowitz A., Droites en position générale dans l’espace projectif. In: Algebraic Geometry, La Rábida, 1981, Lecture Notes in Math., 961, Springer, Berlin, 1982, 169–188 http://dx.doi.org/10.1007/BFb0071282
  • [16] Pistone G., Riccomagno E., Wynn H.P., Algebraic Statistics, Monogr. Statist. Appl. Probab., 89, Chapman & Hall/CRC, Boca Raton, 2001
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-011-0054-7
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