Abstract blowing down

Details Abstract blowing down Abstract blowing down

1998-06-08

arxiv.org/abs/math/9806046v1

Mathematics

Algebraic Geometry

Scientific paper

Assume that $X$ is a surface over an algebraically closed field $k$. Let
$\tilde{X}$ be obtained from $X$ by blowing up a smooth point and let $L$ be
the exceptional curve. Let $\coh(X)$ be the category of coherent sheaves on
$X$. In this note we show how to recover $\coh({X})$ from $\coh(\tilde{X})$, if
we know the object $\Oscr_L(L)$.

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