English

All strictly exceptional collections in $D^b_{coh}(P^m)$ consist of vector bundles

alg-geom 2013-10-29 v2 Algebraic Geometry

Abstract

It is proved that any strictly exceptional collection generating the derived category of coherent sheaves on a smooth projective variety X with \rk K_0(X) = \dim X + 1 constists of locally free sheaves up to a common shift.

Keywords

Cite

@article{arxiv.alg-geom/9507014,
  title  = {All strictly exceptional collections in $D^b_{coh}(P^m)$ consist of vector bundles},
  author = {Leonid Positselski},
  journal= {arXiv preprint arXiv:alg-geom/9507014},
  year   = {2013}
}

Comments

LaTeX 2e, 6 pages, no figures; replaced to correct formatting (amslatex to latex2e transition) and several misprints, no other changes