Examples of non-ample normal bundles
Norman Goldstein (1984)
Compositio Mathematica
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Norman Goldstein (1984)
Compositio Mathematica
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Tommaso De Fernex (1998)
Collectanea Mathematica
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Frédéric Campana, Thomas Peternell (1992)
Compositio Mathematica
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Antonio Lanteri (2000)
Revista Matemática Complutense
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Let X be a smooth complex projective variety of dimension n ≥ 3. A notion of geometric genus p(X,E) for ample vector bundles E of rank r < n on X admitting some regular sections is introduced. The following inequality holds: p(X,E) ≥ h(X). The question of characterizing equality is discussed and the answer is given for E decomposable of corank 2. Some conjectures suggested by the result are formulated.
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 .
Huashi Xia (1995)
Compositio Mathematica
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Christopher Hacon (2000)
Annales de l'institut Fourier
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We give a lower bound for the Seshadri constants of ample vector bundles which depends only on the numerical properties of the Chern classes and on a “stability” condition.