Examples of non-ample normal bundles
Norman Goldstein (1984)
Compositio Mathematica
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Norman Goldstein (1984)
Compositio Mathematica
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Vasile Brînzănescu, Ruxandra Moraru (2005)
Annales de l’institut Fourier
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In this paper, we consider the problem of determining which topological complex rank-2 vector bundles on non-Kähler elliptic surfaces admit holomorphic structures; in particular, we give necessary and sufficient conditions for the existence of holomorphic rank-2 vector bundles on non-{Kä}hler elliptic surfaces.
Hoil Kim (1994)
Manuscripta mathematica
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Sonia Brivio (1993)
Mathematische Zeitschrift
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Michał Szurek, Jarosław A. Wisniewski (1990)
Compositio Mathematica
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Emura, Erika, Kojima, Hideo (2010)
Beiträge zur Algebra und Geometrie
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Tommaso De Fernex (1998)
Collectanea Mathematica
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Ulrich Schlickewei (2010)
Rendiconti del Seminario Matematico della Università di Padova
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Nicole Mestrano (1985)
Annales de l'institut Fourier
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Let be a smooth projective surface, the canonical divisor, a very ample divisor and the moduli space of rank-two vector bundles, -stable with Chern classes and . We prove that, if there exists such that is numerically equivalent to and if is even, greater or equal to , then there is no Poincaré bundle on . Conversely, if there exists such that the number is odd or if is odd, then there exists a Poincaré bundle on .