GW/PT descendent correspondence via vertex operators

Abstract

We propose an explicit formula for the GW/PT descendent correspondence in the stationary case for nonsingular projective 3-folds. The formula, written in terms of vertex operators, is found by studying the 1-leg geometry. We prove the proposal for all nonsingular projective toric 3-folds. An application to the Virasoro constraints for the stationary descendent theory of stable pairs will appear in a sequel.

36 pages, no pictures; few misprints are corrected; to appear in Communications in Mathematical Physics; slight change in the definition of the generating function for GW invariants; many misprints corrected