Abstract blowing down
HTML articles powered by AMS MathViewer
- by Michel Van den Bergh PDF
- Proc. Amer. Math. Soc. 128 (2000), 375-381 Request permission
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 $\mathcal {O}_L(L)$.References
- A. A. Beĭlinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces, I (Luminy, 1981) Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171 (French). MR 751966
- A. I. Bondal, Representations of associative algebras and coherent sheaves, Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989), no. 1, 25–44 (Russian); English transl., Math. USSR-Izv. 34 (1990), no. 1, 23–42. MR 992977, DOI 10.1070/IM1990v034n01ABEH000583
- A. I. Bondal and D. O. Orlov, Semi-orthogonal decompositions for algebraic varieties, MPI preprint, 1996.
- Pierre Gabriel, Des catégories abéliennes, Bull. Soc. Math. France 90 (1962), 323–448 (French). MR 232821
- Dieter Happel, Idun Reiten, and Sverre O. Smalø, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc. 120 (1996), no. 575, viii+ 88. MR 1327209, DOI 10.1090/memo/0575
- M. Van den Bergh, Blowing up of non-commutative smooth surfaces, to appear, 1997.
- —, Blowing up points in the elliptic quantum plane, in preparation, 1998.
Additional Information
- Michel Van den Bergh
- Affiliation: Departement WNI, Limburgs Universitair Centrum, Universitaire Campus, 3590 Diepenbeek, Belgium
- MR Author ID: 176980
- Email: vdbergh@luc.ac.be
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 375-381
- MSC (1991): Primary 14A20, 18E35
- DOI: https://doi.org/10.1090/S0002-9939-99-05078-9
- MathSciNet review: 1628424