Rank 4 vector bundles on the quintic threefold

الأصل · EN

By the results of the author and Chiantini in Math.AG/0110102, on a general quintic threefold X ⊂ P⁴ the minimum integer p for which there exists a positive dimensional family of irreducible rank p vector bundles on X without intermediate cohomology is at least three. In this paper we show that p ≤ 4, by constructing series of positive dimensional families of rank 4 vector bundles on X without intermediate cohomology. The general member of such family is an indecomposable bundle from the extension class Ext¹(E,F), for a suitable choice of the rank 2 ACM bundles E and F on X. The existence of such bundles of rank p = 3 remains under question.