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Stability conditions via spherical objects

Research paper by D. Huybrechts

Indexed on: 08 Jul '11Published on: 08 Jul '11Published in: Mathematische Zeitschrift



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.