# Donaldson–Thomas invariants for complexes on abelian threefolds

@article{Gulbrandsen2013DonaldsonThomasIF, title={Donaldson–Thomas invariants for complexes on abelian threefolds}, author={Martin G. Gulbrandsen}, journal={Mathematische Zeitschrift}, year={2013}, volume={273}, pages={219-236} }

Donaldson–Thomas invariants for moduli spaces M of perfect complexes on an abelian threefold X are usually zero. A better object is the quotient $${K=[M/X\times\widehat{X}]}$$ of complexes modulo twist and translation. Roughly speaking, this amounts to fixing not only the determinant of the complexes in M, but also that of their Fourier–Mukai transform. We modify the standard perfect symmetric obstruction theory for perfect complexes to obtain a virtual fundamental class, giving rise to a DT… Expand

#### 11 Citations

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We study the reduced Donaldson-Thomas theory of abelian threefolds using Bridgeland stability conditions. The main result is the invariance of the reduced Donaldson-Thomas invariants under all… Expand

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Let X be an Abelian threefold. We prove a formula, conjectured by the first author, expressing the Euler characteristic of the generalized Kummer schemes $$K^nX$$KnX of X in terms of the number of… Expand

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