We show that the generating series of generalized Donaldson–Thomas invariants on the local projective plane with any positive rank is described in terms of modular forms and theta type series for indefinite lattices. In particular, it absolutely converges to give a holomorphic function on the upper half plane.
"Generalized Donaldson–Thomas invariants on the local projective plane." J. Differential Geom. 106 (2) 341 - 369, June 2017. https://doi.org/10.4310/jdg/1497405629