EPW Sextics and Hilbert Squares of K3 Surfaces
[Iliev Atanas; Илиев Атанас] 2010 Mathematics Subject Classification: 14J35, 14F05.
Rank 4 vector bundles on the quintic threefold
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...
Rank-two vector bundles on general quartic hypersurfaces in P.
In this paper all non-splitting rank-two vector bundles E without intermediate cohomology on a general quartic hypersurface X in P are classified. In particular, the existence of some curves on a general quartic hypersurface is proved.
ACM bundles on general hypersurfaces in P of low degree.
In this paper we show that on a general hypersurface of degree r = 3,4,5,6 in P a rank 2 vector bundle ε splits if and only if hε(n) = hε(n) = 0 for all n ∈ Z. Similar results for r = 1,2 were obtained in [15], [16] and [2].
Page 1