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Triangulated categories of Gorenstein cyclic quotient singularities
Author(s):
Kazushi
Ueda
Journal:
Proc. Amer. Math. Soc.
136
(2008),
2745-2747.
MSC (2000):
Primary 18E30;
Secondary 16G20
Posted:
April 3, 2008
MathSciNet review:
2399037
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Abstract:
We prove there is an equivalence of derived categories between Orlov's triangulated category of singularities for a Gorenstein cyclic quotient singularity and the derived category of representations of a quiver with relations, which is obtained from a McKay quiver by removing one vertex and half of the arrows. This result produces examples of distinct quivers with relations which have equivalent derived categories of representations.
References:
-
- 1.
- M. Artin and J. J. Zhang.
Noncommutative projective schemes.
Adv. Math., 109(2):228-287, 1994. MR 1304753 (96a:14004) - 2.
- Denis Auroux, Ludmil Katzarkov, and Dmitri Orlov.
Mirror symmetry for weighted projective planes and their noncommutative deformations.
math.AG/0404281, 2004. - 3.
- A. I. Bondal.
Representations of associative algebras and coherent sheaves.
Izv. Akad. Nauk SSSR Ser. Mat., 53(1):25-44, 1989. MR 992977 (90i:14017) - 4.
- Hiroshige Kajiura, Kyoji Saito, and Atsushi Takahashi.
Matrix factorizations and representations of quivers II: type ADE case.
math.AG/0511155, 2005. - 5.
- John McKay.
Graphs, singularities, and finite groups.
In The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979), volume 37 of Proc. Sympos. Pure Math., pages 183-186. Amer. Math. Soc., Providence, R.I., 1980. MR 604577 (82e:20014) - 6.
- D. O. Orlov.
Derived categories of coherent sheaves and triangulated categories of singularities.
math.AG/0503632, 2005. - 7.
- Atsushi Takahashi.
Matrix factorizations and representations of quivers I.
math.AG/0506347, 2005.
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Additional Information:
Kazushi
Ueda
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka, 560-0043, Japan
Email:
kazushi@math.sci.osaka-u.ac.jp
DOI:
10.1090/S0002-9939-08-09470-7
PII:
S 0002-9939(08)09470-7
Received by editor(s):
July 6, 2006,
Received by editor(s) in revised form:
October 6, 2006, and July 8, 2007
Posted:
April 3, 2008
Additional Notes:
The author was supported by the 21st Century COE Program of Osaka University.
Communicated by:
Ted Chinburg
Copyright of article:
Copyright
2008,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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