On the Hilbert function of zero-dimensional schemes in {{\mathbb P}^1 \times {\mathbb P}^1}

• Autores: P. Bonacini, L. Marino
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 62, Fasc. 1, 2011, págs. 57-67
• Idioma: español
• DOI: 10.1007/s13348-010-0004-x
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• Resumen

  • Let {Q = {\mathbb P}^1 \times {\mathbb P}^1} and let {X\subset Q} be a zero-dimensional scheme. The results in this paper give the possibility of computing, under certain hypotheses, the Hilbert function of a zero-dimensional scheme in Q that is not ACM. In particular we show how, under some conditions on X, its Hilbert function changes when we add points to X lying on a (1, 0) or (0, 1)-line. As a particular case we show also that if X is ACM this result holds without any additional hypothesis.

• Referencias bibliográficas
  • Giuffrida S., Maggioni R.: Curves on a smooth quadric. Collect. Math. 54(3), 309–325 (2003)
  • Giuffrida S., Maggioni R., Ragusa A.: On the postulation of 0-dimensional subschemes on a smooth quadric. Pacific J. Math. 155(2), 251–282...
  • Guardo E.: Fat points schemes on a smooth quadric. J. Pure Appl. Algebra 162, 183–208 (2001)
  • Guardo E., Van Tuyl A.: Fat points in {\mathbb P^1\times \mathbb P^1} and their Hilbert functions. Can. J. Math. 56(4), 716–741 (2004)
  • Van Tuyl A.: The border of the Hilbert function of a set of points in {{\mathbb P}^{n_1}\times\dots\times{\mathbb P}^{n_k}} . J. Pure Appl....
  • Van Tuyl A.: The Hilbert function of ACM set of points in {{\mathbb P}^{n_1}\times\dots\times{\mathbb P}^{n_k}} . J. Algebra 264, 420–441...
  • Van Tuyl, A.: An appendix to a paper of Catalisano, Geramita, Gimigliano: the Hilbert function of generic sets of 2-fat points in {{\mathbb...