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Maximal rationally connected fibrations and movable curves

Luis E. Solá Conde, Matei Toma (2009)

Annales de l’institut Fourier

A well known result of Miyaoka asserts that a complex projective manifold is uniruled if its cotangent bundle restricted to a general complete intersection curve is not nef. Using the Harder-Narasimhan filtration of the tangent bundle, it can moreover be shown that the choice of such a curve gives rise to a rationally connected foliation of the manifold. In this note we show that, conversely, a movable curve can be found so that the maximal rationally connected fibration of the manifold may be recovered...

Minimal resolution of general stable rank-2 vector bundles on P 2

Carla Dionisi, Marco Maggesi (2003)

Bollettino dell'Unione Matematica Italiana

We study general elements of moduli spaces M P 2 2 , c 1 , c 2 of rank-2 stable holomorphic vector bundles on P 2 and their minimal free resolutions. Incidentally, a quite easy proof of the irreducibility of M P 2 2 , c 1 , c 2 is shown.

Minimal sections of conic bundles

Atanas Iliev (1999)

Bollettino dell'Unione Matematica Italiana

Sia p : X P 2 un fibrato in coniche standard con curva discriminante Δ di grado d . La varietà delle sezioni minime delle superfici p - 1 C , dove C è una curva di grado d - 3 , si spezza in due componenti C + e C - . Si prova che, mediante la mappa di Abel-Jacobi Φ , una di queste componenti domina la Jacobiana intermedia J X , mentre l'altra domina il divisore theta Θ J X . Questi risultati vengono applicati ad alcuni threefold di Fano birazionalmente equivalenti a un fibrato in coniche. In particolare si prova che il generico...

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