Rank 4 vector bundles on the quintic threefold
Carlo Madonna
Open Mathematics, Tome 3 (2005), p. 404-411 / Harvested from The Polish Digital Mathematics Library
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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 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.

Publié le : 2005-01-01
EUDML-ID : urn:eudml:doc:268833 
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     author = {Carlo Madonna},
     title = {Rank 4 vector bundles on the quintic threefold},
     journal = {Open Mathematics},
     volume = {3},
     year = {2005},
     pages = {404-411},
     zbl = {1106.14029},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475915}
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Carlo Madonna. Rank 4 vector bundles on the quintic threefold. Open Mathematics, Tome 3 (2005) pp. 404-411. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475915/

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