Logarithmic sheaves attached to arrangements of hyperplanes

  title={Logarithmic sheaves attached to arrangements of hyperplanes},
  author={Igor Dolgachev},
  journal={Journal of Mathematics of Kyoto University},
  • I. Dolgachev
  • Published 1 August 2005
  • Mathematics
  • Journal of Mathematics of Kyoto University
A reduced divisor on a nonsingular variety defines the sheaf of logarithmic 1-forms. We introduce a certain coherent sheaf whose double dual coincides with this sheaf. It has some nice properties, for example, the residue exact sequence still holds even when the divisor is singular, and also it has a simple locally free resolution. We specialize to the case when the divisor is an arrangement of hyperplanes in projective space, and relate the properties of stability of the sheaf with the… 
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