Communications in Analysis and Geometry

Volume 19 (2011)

Number 4

Semi-perfect obstruction theory and Donaldson–Thomas invariants of derived objects

Pages: 807 – 830



Huai-liang Chang (Department of Mathematics, Hong Kong University of Science and Technology)

Jun Li (Department of Mathematics, Stanford University)


We introduce a semi-perfect obstruction theory of a Deligne–Mumford stack $X$ that consists of localperfect obstruction theories with a global obstruction sheaf. We construct the virtual cycle of aDeligne–Mumford stack with a semi-perfect obstruction theory. We use semi-perfect obstruction theoryto construct virtual cycles of moduli of derived objects on Calabi–Yau threefolds.

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