Abstract blowing down
Michel Van den Bergh
- 08 Jul 1999
- Vol. 128, Iss: 2, pp 375-381
TL;DR: In this paper, the authors show how to recover coherent sheaves from a smooth point in an algebraically closed field if we know the object Oscr_L(L)(L).
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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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References
•Book
Tilting in Abelian Categories and Quasitilted Algebras
Dieter Happel,Idun Reiten,O SmaløSverre +2 more
- 01 Jan 1996
797
Representation of associative algebras and coherent sheaves
TL;DR: In this paper, it was shown that a triangulated category generated by a strong exceptional collection is equivalent to the derived category of modules over an algebra of homomorphisms of this collection.
488
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Blowing up non-commutative smooth surfaces
TL;DR: In this paper, it was shown that under certain conditions a point on a non-commutative surface can be blown up, which yields a new surface which is in a certain sense birational to the original one.
10
Des catégories abéliennes
TL;DR: The Bulletin de la S. M. F. as mentioned in this paper implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/legal.html).