Regularity bounds by minimal generators and Hilbert function

• Autores: F. Cioffi, M. G. Marinari, Luciana Ramella
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 60, Fasc. 1, 2009, págs. 89-100
• Idioma: español
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• Resumen

  • Let $\rho_C$ be the regularity of the Hilbert function of a projective curve $C$ in ${\bf P}^n_K$ over an algebraically closed field $K$ and $\beta_1,\ldots,\beta_{n-1}$ be degrees for which there exists a complete intersection of type $(\beta_1,\ldots,\beta_{n-1})$ containing properly $C$. Then the Castelnuovo-Mumford regularity of $C$ is upper bounded by $\max\{\rho_C+1 \beta_1+ \ldots+ \beta_{n-1}-(n-1)\}$. We investigate the sharpness of the above bound, which is achieved by curves algebraically linked to ones having degenerate general hyperplane section.