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ACM bundles on general hypersurfaces in P5 of low degree.

Luca Chiantini, Carlo K. Madonna (2005)

Collectanea Mathematica

In this paper we show that on a general hypersurface of degree r = 3,4,5,6 in P5 a rank 2 vector bundle ε splits if and only if h1ε(n) = h2ε(n) = 0 for all n ∈ Z. Similar results for r = 1,2 were obtained in [15], [16] and [2].

ACM bundles, quintic threefolds and counting problems

N. Mohan Kumar, Aroor Rao (2012)

Open Mathematics

We review some facts about rank two arithmetically Cohen-Macaulay bundles on quintic threefolds. In particular, we separate them into seventeen natural classes, only fourteen of which can appear on a general quintic. We discuss some enumerative problems arising from these.

ACM embeddings of curves of a quadric surface

S. Giuffrida, R. Maggioni, R. Re (2007)

Collectanea Mathematica

Let C be a smooth integral projective curve admitting two pencils ga1 and gb1 such that ga1 + gb1 is birational. We give conditions in order that the complete linear system |sga1 + rgb1| be normally generated or very ample.

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