Ample vector bundles
Robin Hartshorne (1966)
Publications Mathématiques de l'IHÉS
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Robin Hartshorne (1966)
Publications Mathématiques de l'IHÉS
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Edoardo Ballico, Jarosław A. Wisniewski (1996)
Compositio Mathematica
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Laura Costa, Rosa Miró-Roig (2012)
Open Mathematics
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This paper aims to construct a full strongly exceptional collection of line bundles in the derived category D b(X), where X is the blow up of ℙn−r ×ℙr along a multilinear subspace ℙn−r−1×ℙr−1 of codimension 2 of ℙn−r ×ℙr. As a main tool we use the splitting of the Frobenius direct image of line bundles on toric varieties.
Carlo Madonna (2000)
Revista Matemática Complutense
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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.
N. Mohan Kumar, Aroor Rao (2012)
Open Mathematics
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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.
Marcos Jardim, Vitor Silva (2012)
Open Mathematics
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We establish a decomposability criterion for linear sheaves on ℙn. Applying it to instanton bundles, we show, in particular, that every rank 2n instanton bundle of charge 1 on ℙn is decomposable. Moreover, we provide an example of an indecomposable instanton bundle of rank 2n − 1 and charge 1, thus showing that our criterion is sharp.
Alexander Kuznetsov (2012)
Open Mathematics
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We introduce the notion of an instanton bundle on a Fano threefold of index 2. For such bundles we give an analogue of a monadic description and discuss the curve of jumping lines. The cases of threefolds of degree 5 and 4 are considered in a greater detail.
Madonna, C. (1998)
Rendiconti del Seminario Matematico
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Michael Schneider (1978-1979)
Séminaire Bourbaki
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Dimitri Markushevich, Alexander Tikhomirov, Günther Trautmann (2012)
Open Mathematics
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We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundles and connections in differential geometry. The new moduli spaces are algebraic spaces arising as quotients by group actions according to a result of Kollár. As an example, the compactification of the space of stable rank 2 vector bundles with Chern classes c...
Laurent Gruson, Frédéric Han (2012)
Open Mathematics
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We review a construction of Ellingsrud-Strømme relating instantons of charge n on the ordinary projective space and theta-characteristics on a plane curve of degree n with some extra-structure.