Duke Mathematical Journal

Stability conditions on $K3$ surfaces

Tom Bridgeland

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


This article contains a description of one connected component of the space of stability conditions on the bounded derived category of coherent sheaves on a complex algebraic K$3$ surface

Article information

Duke Math. J. Volume 141, Number 2 (2008), 241-291.

First available in Project Euclid: 17 January 2008

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 18E30: Derived categories, triangulated categories 14J28: $K3$ surfaces and Enriques surfaces


Bridgeland, Tom. Stability conditions on K 3 surfaces. Duke Math. J. 141 (2008), no. 2, 241--291. doi:10.1215/S0012-7094-08-14122-5. https://projecteuclid.org/euclid.dmj/1200601792.

Export citation


  • W. Barth, C. Peters, and A. Van De Ven, Compact Complex Surfaces, Ergeb. Math. Grenzgeb. (3) 4, Springer, Berlin, 1984.
  • A. A. Beĭlinson, J. Bernstein, and P. Deligne, ``Faisceaux pervers'' in Analysis and Topology on Singular Spaces, I (Luminy, France, 1981), Astérisque 100, Soc. Math. France, Montrouge, 1983, 5--171.
  • T. Bridgeland, Stability conditions on triangulated categories, to appear in Ann. of Math. (2), preprint.
  • —, Spaces of stability conditions, preprint.
  • T. Bridgeland and A. Macioica, Complex surfaces with equivalent derived categories, Math. Z. 236 (2001), 677--697.
  • —, Fourier-Mukai transforms for $K3$ and elliptic fibrations, J. Algebraic Geom. 11 (2002), 629--657.
  • M. R. Douglas, ``Dirichlet branes, homological mirror symmetry, and stability'' in Proceedings of the International Congress of Mathematicians, Vol. III (Beijing, 2002), Higher Ed. Press, Beijing, 2002, 395--408.
  • S. I. Gelfand and Y. I. Manin, Methods of Homological Algebra, Springer, Berlin, 1996.
  • D. Happel, I. Reiten, and S. O. Smalø, Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc. 120 (1996), no. 575.
  • D. Huybrechts, personal communication, July 2006.
  • K. Matsuki and R. Wentworth, Mumford-Thaddeus principle on the moduli space of vector bundles on an algebraic surface, Internat. J. Math. 8 (1997), 97--148.
  • S. Mukai, Duality between $\D(X)$ and $\D(\hat{X})$ with its application to Picard sheaves, Nagoya Math. J. 81 (1981), 153--175.
  • —, ``Fourier functor and its application to the moduli of bundles on an abelian variety'' in Algebraic Geometry (Sendai, Japan, 1985), Adv. Stud. Pure Math. 10, North-Holland, Amsterdam, 1987, 515--550.
  • —, ``On the moduli space of bundles on $K3$ surfaces, I'' in Vector Bundles on Algebraic Varieties (Bombay, 1984), Tata Inst. Fund. Res. Stud. Math. 11, Tata Inst. Fund. Res., Bombay, 1987, 341--413.
  • D. O. Orlov, ``Equivalences of derived categories and $K3$ surfaces'' in Algebraic Geometry, Vol. 7, J. Math. Sci. (New York) 84, Kluwer, New York, 1997, 1361--1381.
  • P. Seidel and R. Thomas, Braid group actions on derived categories of coherent sheaves, Duke Math. J. 108 (2001), 37--108.
  • B. Szendröi, ``Diffeomorphisms and families of Fourier-Mukai transforms in mirror symmetry'' in Applications of Algebraic Geometry to Coding Theory, Physics and Computation (Eilat, Israel, 2001), NATO Sci. Ser. II Math. Phys. Chem. 36, Kluwer, Dordrecht, Netherlands, 2001, 317--337.
  • K. Yoshioka, Chamber structure of polarizations and the moduli of stable sheaves on a ruled surface, Internat. J. Math. 7 (1996), 411--431.
  • —, Moduli spaces of stable sheaves on abelian surfaces, Math. Ann. 321 (2001), 817--884.