A splitting criterion for rank 2 vector bundles on a general sextic threefold

Abstract

In this paper we show that on a general sextic hypersurface $X\subset {\mathbf{P}}^4$, a rank 2 vector bundle $E$ splits if and only if $h^1(E(n))=0$ for any $n\in \mathbf{Z}$. We get thus a characterization of complete intersection curves in $X$