Naive motivic Donaldson--Thomas type Hirzebruch classes and some problems

Journal of Singularities
volume 10 (2014), 26-53

Received 21 January 2013. Received in revised form 26 November 2013.

DOI: 10.5427/jsing.2014.10b

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Abstract:

Donaldson-Thomas invariant is expressed as the weighted Euler characteristic of the so-called Behrend (constructible) function. In 2009, Behrend introduced a Donaldson-Thomas type invariant for a morphism. Motivated by this invariant, we extend the motivic Hirzebruch class to naive Donaldson-Thomas type analogues. We also discuss a categorification of the Donaldson-Thomas type invariant for a morphism from a bivariant-theoretic viewpoint, and we finally pose some related questions for further investigations.

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