Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Triangulated categories of Gorenstein cyclic quotient singularities

Author: Kazushi Ueda
Journal: Proc. Amer. Math. Soc. 136 (2008), 2745-2747
MSC (2000): Primary 18E30; Secondary 16G20
Published electronically: April 3, 2008
MathSciNet review: 2399037
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 18E30, 16G20

Retrieve articles in all journals with MSC (2000): 18E30, 16G20

Additional Information

Kazushi Ueda
Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Machikaneyama 1-1, Toyonaka, Osaka, 560-0043, Japan

Received by editor(s): July 6, 2006
Received by editor(s) in revised form: October 6, 2006, and July 8, 2007
Published electronically: April 3, 2008
Additional Notes: The author was supported by the 21st Century COE Program of Osaka University.
Communicated by: Ted Chinburg
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society