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arXiv · 0910.5477

Non-commutative Donaldson-Thomas theory and vertex operators

Kentaro Nagao
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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.

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Kentaro Nagao. 2010-11-23. Non-commutative Donaldson-Thomas theory and vertex operators. https://arxiv.org/abs/0910.5477

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