Journal of Algebraic Geometry

Author(s): Daniel Huybrechts
Journal: J. Algebraic Geom. 17 (2008), 375-400.
Posted: December 6, 2007
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Abstract: The paper attempts to shed more light on a particular class of stability conditions on

surfaces constructed by Tom Bridgeland. The hearts of the underlying t-structures turn out to be significant invariants of the surface. We prove that two

surfaces

and

are derived equivalent if and only if there exist complexified polarizations $B+i\omega$ and $B'+i\omega'$ such that the associated abelian categories $\mathcal{A}(\exp(B+i\omega))$ and $\mathcal{K}(\exp(B'+i\omega'))$ are equivalent. We study in detail the minimal objects of $\mathcal{A}(\exp(B+i\omega))$ and investigate stability under the Fourier-Mukai transform.

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