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Rank 4 vector bundles on the quintic threefold

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Madonna C.

Open Mathematics

2005

tom 3

nr 3

404-411

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 class Ext 1 (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.

Ograniczanie wyników

1 Open Mathematics

1 Madonna C.

1 2005

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Rank 4 vector bundles on the quintic threefold