Non-commutative Donaldson–Thomas theory and vertex operators

Nagao, Kentaro

doi:10.2140/gt.2011.15.1509

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1364-0380 (online)

ISSN 1465-3060 (print)

Author Index

To Appear

Other MSP Journals

Non-commutative Donaldson–Thomas theory and vertex operators

Kentaro Nagao

Geometry & Topology 15 (2011) 1509–1543

DOI: 10.2140/gt.2011.15.1509

Abstract

In [K Nagao, Refined open non-commutative Donaldson–Thomas theory for small toric Calabi–Yau 3–folds, Pacific J. Math. (to appear), arXiv:0907.3784], we introduced a variant of non-commutative Donaldson–Thomas theory in a combinatorial way, which is related to the 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 [A Okounkov, N Reshetikhin, C Vafa, Quantum Calabi–Yau and classical crystals, from: “The unity of mathematics”, Progr. Math., Birkhäuser (2006) 597–618] and [B Young, Generating functions for colored 3D Young diagrams and the Donaldson–Thomas invariants of orbifolds, Duke Math. J. 152 (2010) 115–153]. 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.

Keywords

Donaldson–Thomas theory, wall-crossing, vertex operator

Mathematical Subject Classification 2000

Primary: 14N35

References

Publication

Received: 17 November 2009

Revised: 23 April 2011

Accepted: 3 June 2011

Published: 3 August 2011

Proposed: Jim Bryan

Seconded: Richard Thomas, Simon Donaldson

Authors

Kentaro Nagao
RIMS Kyoto University Kyoto 606-8502 Japan

Volume 15, issue 3 (2011)