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Stability conditions via spherical objects

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Abstract

An object in the bounded derived category Db(X) of coherent sheaves on a complex projective K3 surface X is spherical if it is rigid and simple. Although spherical objects form only a discrete set in the moduli stack of complexes, they determine much of the structure of X and Db(X). Here we show that a stability condition on Db(X) is determined by the stability of spherical objects.

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Authors and Affiliations

  1. Mathematisches Institut, Universität Bonn, Endenicher Alle 60, 53115, Bonn, Germany

    D. Huybrechts

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  1. D. Huybrechts
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Correspondence to D. Huybrechts.

Additional information

This work was supported by the SFB/TR 45 ‘Periods, Moduli Spaces and Arithmetic of Algebraic Varieties’ of the DFG (German Research Foundation). The hospitality and financial support of the Mathematical Institute Oxford is gratefully acknowledged.

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Huybrechts, D. Stability conditions via spherical objects. Math. Z. 271, 1253–1270 (2012). https://doi.org/10.1007/s00209-011-0914-7

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  • DOI: https://doi.org/10.1007/s00209-011-0914-7

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