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This article is an attempt to briefly introduce some of the results fromarXiv:1011.6342 on development of a higher rank analog of thePandharipande-Thomas theory of stable pairs on a Calabi-Yau threefold X. Moreprecisely, we develop a moduli theory for highly frozen triples given by thedata O^r-->F for r>1 where F is a sheaf of pure dimension 1. The moduli spaceof such objects does not naturally determine an enumerative theory. Instead, webuild a zero-dimensional virtual fundamental class by truncating adeformation-obstruction theory coming from the moduli of objects in the derivedcategory of X. We briefly include the results of calculations in thisenumerative theory for local P^1 using the Graber-Pandharipande virtuallocalization technique. We emphasize that in this article we merely include thestatement of our theorems and illustrate the final result of some of thecomputations. The proofs and more detailed calculations in arXiv:1011.6342 willappear elsewhere.

An introduction to the theory of Higher rank stable pairs and Virtual localization