English

Semi-Stable Chow-Hall Algebras of Quivers and Quantized Donaldson-Thomas Invariants

Representation Theory 2018-08-08 v2 Algebraic Geometry

Abstract

The semi-stable ChowHa of a quiver with stability is defined as an analog of the Cohomological Hall algebra of Kontsevich and Soibelman via convolution in equivariant Chow groups of semi-stable loci in representation varieties of quivers. We prove several structural results on the semi-stable ChowHa, namely isomorphism of the cycle map, a tensor product decomposition, and a tautological presentation. For symmetric quivers, this leads to an identification of their quantized Donaldson-Thomas invariants with the Chow-Betti numbers of moduli spaces.

Keywords

Cite

@article{arxiv.1512.03748,
  title  = {Semi-Stable Chow-Hall Algebras of Quivers and Quantized Donaldson-Thomas Invariants},
  author = {H. Franzen and M. Reineke},
  journal= {arXiv preprint arXiv:1512.03748},
  year   = {2018}
}

Comments

23 pages; v2: Fixed an error in the proof of Thm. 5.1, generalized Thm. 6.1 to arbitrary quivers (not just symmetric ones)