Non-commutative Donaldson-Thomas theory and vertex operators
Abstract
In arXiv:0907.3784, we introduced a variant of non-commutative Donaldson-Thomas theory in a combinatorial way, which is related with topological vertex by a wall-crossing phenomenon. In this paper, we (1) provide an alternative definition in a geometric way, (2) show that the two definitions agree with each other and (3) compute the invariants using the vertex operator method, following Okounkov-Reshetikhin-Vafa and Young. The stability parameter in the geometric definition determines the order of the vertex operators and hence we can understand the wall-crossing formula in non-commutative Donaldson-Thomas theory as the commutator relation of the vertex operators.
Cite
@article{arxiv.0910.5477,
title = {Non-commutative Donaldson-Thomas theory and vertex operators},
author = {Kentaro Nagao},
journal= {arXiv preprint arXiv:0910.5477},
year = {2010}
}
Comments
29 pages, 4 figures, some minor changes, descriptions about symmetric obstruction theory (section 5.2 and 6.1) are improved