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

Mathematics – Algebraic Geometry

Scientific paper

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AMS-LaTeX v.1.1, 6 pages, no figures

Scientific paper

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.

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