Donaldson-Thomas type invariants via microlocal geometry. (English) Zbl 1191.14050

Behrend, Kai

Ann. Math. (2) 170, No. 3, 1307-1338 (2009).

Donaldson-Thomas invariants are the virtual counts of stable sheaves on Calabi-Yau threefolds. In this work, the author proves that the Donaldson-Thomas type invariants are equal to weighted Euler characteristics of their moduli space. In fact such invariants depend only on the scheme structure of the moduli space, not the symmetric obstruction theory used to define them.
In this work, the author also introduce new invariants generalizing Donaldson-Thomas type invariants to moduli problems with open moduli space.

Reviewer: Vehbi Emrah Paksoy (Ft. Lauderdale)

MSC:

14J32	Calabi-Yau manifolds (algebro-geometric aspects)
14N35	Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)

Keywords:

Donaldson-Thomas invariants; microlocal geometry; virtual Euler characteristic; constructible function; symmetric obstruction theories

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