Van den Bergh, Michel Abstract blowing down. (English) Zbl 0929.14004 Proc. Am. Math. Soc. 128, No. 2, 375-381 (2000). 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 \(\mathcal{O}_L(L)\). Cited in 2 Documents MSC: 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010) 18E40 Torsion theories, radicals 18E30 Derived categories, triangulated categories (MSC2010) Keywords:blowing down; category of coherent sheaves PDFBibTeX XMLCite \textit{M. Van den Bergh}, Proc. Am. Math. Soc. 128, No. 2, 375--381 (2000; Zbl 0929.14004) Full Text: DOI arXiv