Vector bundles of finite rank on complete intersections of finite codimension in ind-Grassmannians

Svetlana Ermakova

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By the results of the author and Chiantini in [3], on a general quintic threefold X⊂P 4 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...