A vanishing theorem for the ideal sheaf of codimension two subvarieties of \bf P^n

Abstract

Sia X $\subset\mathbf{P^{\textrm{n}}}$ una varietà di codimensione 2. Proviamo che H$^{q}$($\mathcal{I}_{x}(t))$=0 per n$\geq$q +4t+3, e 1$\leq q\leq n-2$

Let X $\subset\mathbf{P^{\textrm{n}}}$ be a 2-codimensional variety. We prove that H$^{q}$($\mathcal{I}_{x}(t))$=0 for n$\geq$q +4t+3, and 1$\leq q\leq n-2$