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Poincaré bundles for projective surfaces

Nicole Mestrano (1985)

Annales de l'institut Fourier

Let X be a smooth projective surface, K the canonical divisor, H a very ample divisor and M H ( c 1 , c 2 ) the moduli space of rank-two vector bundles, H -stable with Chern classes c 1 and c 2 . We prove that, if there exists c 1 ' such that c 1 is numerically equivalent to 2 c 1 ' and if c 2 - 1 4 c 1 2 is even, greater or equal to H 2 + H K + 4 , then there is no Poincaré bundle on M H ( c 1 , c 2 ) × X . Conversely, if there exists c 1 ' such that the number c 1 ' · c 1 is odd or if 1 2 c 1 2 - 1 2 c 1 · K - c 2 is odd, then there exists a Poincaré bundle on M H ( c 1 , c 2 ) × X .

Positivity on subvarieties and vanishing of higher cohomology

Alex Küronya (2013)

Annales de l’institut Fourier

We study the relationship between positivity of restriction of line bundles to general complete intersections and vanishing of their higher cohomology. As a result, we extend classical vanishing theorems of Kawamata–Viehweg and Fujita to possibly non-nef divisors.

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