Three-dimensional flops and noncommutative rings
By Michel van den Bergh. 2002
329 citations recorded by the source corpus.
Limburgs Univ Ctr, Dept Math, B-3590 Diepenbeek, Belgium.Van den Bergh, M, Limburgs Univ Ctr, Dept Math, Univ Campus, B-3590 Diepenbeek, Belgium.vdbergh@luc.ac.be
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c0bb4c193581fcc8e57b29bf47b56716358b76d1
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In Geometry and Topology
- Yukinobu Toda
- M. Wemyss
- Osamu Iyama
- T. Bridgeland
- Y. Kawamata
- Balázs Szendrői
- Emanuele Macrì
- Arend Bayer
In Mathematical Physics
- Yukinobu Toda
- Osamu Iyama
- M. Wemyss
- T. Bridgeland
- Balázs Szendrői
- Y. Kawamata
- Emanuele Macrì
- Arend Bayer
Citations in the corpus
- Stability conditions and extremal contractions (2012, background): “When f(D) is a curve, Van den Bergh [14] shows that X is derived equivalent to a certain coherent OY -algebras A , and the perverse heart in [10] corresponds to the category of right A -modules.”
- Mutation in triangulated categories and rigid Cohen–Macaulay modules (2006, methodology): “We should refer to the fact [38, 40] that the rigid Cohen-Macaulay modules have deep relevance to noncommutative crepant resolutions introduced by Van den Bergh [60, 61].”
- Curve counting theories via stable objects Ⅱ : DT/ncDT flop formula (2009, methodology): “By Van den Bergh [7], the abelian categories pPer(X/Y ) are related to sheaves of non-commutative algebras on Y .”
- Non-commutative Donaldson-Thomas theory and the conifold (2007, background): “It is known [24] that D(X/Z) is equivalent to the derived category Dnilp(A−Mod) of complexes of finitely generated A-modules with locally nilpotent cohomology modules.”
- Derived categories of toric varieties III (2006, background): “The derived equivalence in the case of flops (case (c) with KX +B = KY +C) was proved for general (nontoric) case under the additional assumptions as follows: if dimX = 3 andX is smooth by Bridgeland ([5]), if dimX = 3 andX has only Gorenstein terminal singularities by Chen ([8]) and Van den Bergh (”
- Derived categories of coherent sheaves (2006, background): “A more direct proof has since been found by Kawamata [26] using results of Van den Bergh [50].”