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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 .

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