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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Abstract blowing down


Author: Michel Van den Bergh
Journal: Proc. Amer. Math. Soc. 128 (2000), 375-381
MSC (1991): Primary 14A20, 18E35
Published electronically: July 8, 1999
MathSciNet review: 1628424
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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 $\operatorname{coh}(X)$ be the category of coherent sheaves on $X$. In this note we show how to recover $\operatorname{coh}({X})$ from $\operatorname{coh}(\tilde{X})$, if we know the object $\mathcal{O}_L(L)$.


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Additional Information

Michel Van den Bergh
Affiliation: Departement WNI, Limburgs Universitair Centrum, Universitaire Campus, 3590 Diepenbeek, Belgium
Email: vdbergh@luc.ac.be

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05078-9
PII: S 0002-9939(99)05078-9
Keywords: Blowing down
Received by editor(s): April 8, 1998
Published electronically: July 8, 1999
Additional Notes: The author is a director of research at the NFWO
Communicated by: Lance W. Small
Article copyright: © Copyright 1999 American Mathematical Society