Resumen de Regularity bounds by minimal generators and Hilbert function

F. Cioffi, M. G. Marinari, Luciana Ramella

• 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.