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Abstract blowing down. (English) Zbl 0929.14004

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

MSC:

14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
18E40 Torsion theories, radicals
18E30 Derived categories, triangulated categories (MSC2010)
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