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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Maciocia, Antony and Piyaratne, Dulip 2016. Fourier–Mukai transforms and Bridgeland stability conditions on abelian threefolds II. International Journal of Mathematics, Vol. 27, Issue. 01, p. 1650007.


    Sawon, Justin 2016. Moduli spaces of sheaves on K3 surfaces. Journal of Geometry and Physics,


    Yanagida, Shintarou and Yoshioka, Kōta 2014. Bridgeland’s stabilities on abelian surfaces. Mathematische Zeitschrift, Vol. 276, Issue. 1-2, p. 571.


    Minamide, H. Yanagida, S. and Yoshioka, K. 2013. Some Moduli Spaces of Bridgeland's Stability Conditions. International Mathematics Research Notices,


    Maciocia, A. and Meachan, C. 2012. Rank 1 Bridgeland Stable Moduli Spaces on A Principally Polarized Abelian Surface. International Mathematics Research Notices,


    Yoshioka, Kōta 2009. Fourier–Mukai transform on abelian surfaces. Mathematische Annalen, Vol. 345, Issue. 3, p. 493.


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Stability and the Fourier–Mukai transform II

  • Kōta Yoshioka (a1)
  • DOI: http://dx.doi.org/10.1112/S0010437X08003758
  • Published online: 01 January 2009
Abstract
Abstract

We consider the problem of preservation of stability under the Fourier–Mukai transform ℱ:D(X)→D(Y ) on an abelian surface and a K3 surface. If Y is the moduli space of μ-stable sheaves on X with respect to a polarization H, we have a canonical polarization on Y and we have a correspondence between (X,H) and . We show that the stability with respect to these polarizations is preserved under ℱ, if the degree of stable sheaves on X is sufficiently large.

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[2]T. Bridgeland , Equivalences of triangulated categories and Fourier–Mukai transforms, Bull. London Math. Soc. 31 (1999), 2534, math.AG/9809114.

[3]T. Bridgeland , Stability conditions on K3 surfaces, Duke Math. J. 141 (2008), 241291, math.AG/0307164.

[4]D. Huybrechts , Derived and abelian equivalence of K3 surfaces, J. Algebraic Geom. 17 (2008), 375400, math.AG/0604150.

[5]D. Huybrechts and P. Stellari , Equivalences of twisted K3 surfaces, Math. Ann. 332 (2005), 901936, math.AG/0409030.

[8]D. Orlov , Equivalences of derived categories and K3 surfaces, Algebraic geometry, 7. J. Math. Sci. (New York) 84 (1997), 13611381, alg-geom/9606006.

[9]N. Onishi and K. Yoshioka , Singularities on the 2-dimensional moduli spaces of stable sheaves on K3 surfaces, Internat. J. Math. 14 (2003), 837864, math.AG/0208241.

[10]H. Terakawa , The k-very ampleness and k-spannedness on polarized abelian surfaces, Math. Nachr. 195 (1998), 237250.

[13]K. Yoshioka , Moduli spaces of stable sheaves on abelian surfaces, Math. Ann. 321 (2001), 817884, math.AG/0009001.

[16]K. Yoshioka , Stability and the Fourier–Mukai transform I, Math. Z. 245 (2003), 657665.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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