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

@article{Bussi2014NaiveMD,
title={Naive motivic Donaldson-Thomas type Hirzebruch classes and some problems},
author={Vittoria Bussi and Shoji Yokura},
journal={arXiv: Algebraic Geometry},
year={2014}
}
• Published 20 June 2013
• Mathematics
• arXiv: Algebraic Geometry
Donaldson-Thomas invariant is expressed as the weighted Euler characteristic of the so-called Behrend (constructible) function. In (2) Behrend introduced a Donaldson-Thomas type invariant for a mor- phism. 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…
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## References

SHOWING 1-10 OF 51 REFERENCES
Donaldson-Thomas type invariants via microlocal geometry
We prove that Donaldson-Thomas type invariants are equal to weighted Euler characteristics of their moduli spaces. In particular, such invariants depend only on the scheme structure of the moduli
Gromov–Witten theory and Donaldson–Thomas theory, I
• Mathematics
Compositio Mathematica
• 2006
We conjecture an equivalence between the Gromov–Witten theory of 3-folds and the holomorphic Chern–Simons theory of Donaldson and Thomas. For Calabi–Yau 3-folds, the equivalence is defined by the
Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Mathematics
• 2008
We define new invariants of 3d Calabi-Yau categories endowed with a stability structure. Intuitively, they count the number of semistable objects with fixed class in the K-theory of the category
Motivic Donaldson-Thomas invariants: Summary of results
• Mathematics
• 2009
This is a short summary of main results of our paper arXiv:0811.2435 where the concept of motivic Donaldson-Thomas invariant was introduced. It also contains a discussion of some open questions from
A generalized Verdier-type Riemann-Roch theorem for Chern-Schwartz-MacPherson classes
We give a general formula for the defect appearing in the Verdier-type Riemann-Roch formula for Chern-Schwartz-MacPherson classes in the case of a regular embedding. Our proof of this formula uses
Generalized Donaldson-Thomas invariants
This is a survey of the book arXiv:0810.5645 with Yinan Song. Let X be a Calabi-Yau 3-fold over C. The Donaldson-Thomas invariants of X are integers DT^a(t) which count stable sheaves with Chern
Characteristic Classes of Hypersurfaces and Characteristic Cycles
• Mathematics
• 1998
We give a new formula for the Chern-Schwartz-MacPherson class of a hypersurface in a nonsigular compact complex analytic variety. In particular this formula generalizes our previous result on the
HIRZEBRUCH CLASSES AND MOTIVIC CHERN CLASSES FOR SINGULAR SPACES
• Mathematics
• 2005
In this paper we study some new theories of characteristic homology classes of singular complex algebraic (or compactifiable analytic) spaces. We introduce a motivic Chern class transformationmCy: