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

Vittoria Bussi and Shoji Yokura

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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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.

Author(s) information:

Vittoria Bussi Shoji Yokura
The Mathematical Institute Dept. of Mathematics and Computer Science
24-29 St. Giles Faculty of Science
Oxford, OX1 3LB, U.K. Kagoshima University
21-35 Korimoto 1-chome
Kagoshima 890-0065, Japan
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