ACM vector bundles on prime Fano threefolds and complete intersection Calabi Yau threefolds

摘要

In this paper we derive a list of all the possible indecomposable normalizedrank--two vector bundles without intermediate cohomology on the prime Fanothreefolds and on the complete intersection Calabi Yau threefolds, say $V$, ofPicard number $\rho=1$. For any such bundle $\E$, if it exists, we find theprojective invariants of the curves $C \subset V$ which are the zero-locus ofgeneral global sections of $\E$. In turn, a curve $C \subset V$ with suchinvariants is a section of a bundle $\E$ from our lists. This way we reduce theproblem for existence of such bundles on $V$ to the problem for existence ofcurves with prescribed properties contained in $V$. In part of the cases in ourlists the existence of such curves on the general $V$ is known, and we statethe question about the existence on the general $V$ of any type of curves fromthe lists.