Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology

Details Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology Vector bundles on Hirzebruch surfaces whose twists by a non-ample line bundle have natural cohomology

2007-10-18

arxiv.org/abs/0710.3494v2

Mathematics

Algebraic Geometry

7 pages, no figures, to appear on Cent. Eur. J. Math

Scientific paper

Here we study vector bundles $E$ on the Hirzebruch surface $F_e$ such that
their twists by a spanned, but not ample, line bundle $M = \mathcal
{O}_{F_e}(h+ef)$ have natural cohomology, i.e. $h^0(F_e,E(tM)) >0$ implies
$h^1(F_e,E(tM)) = 0$.

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