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Abstract blowing down

Michel Van den Bergh
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Abstract

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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Michel Van den Bergh. 1998-06-08. Abstract blowing down. https://arxiv.org/abs/math/9806046

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