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.