GENERALIZED DONALDSON-THOMAS INVARIANTS OF 2-DIMENSIONAL SHEAVES ON LOCAL P2

ABSTRACT. Let X be the total space of the canonical bundle of P2. We study the generalized Donaldson-Thomas invariants defined in [JS11] of the moduli spaces of the 2-dimensional Gieseker semistable sheaves on X with first Chern class equal to k times the class of the zero section of X. When k = 1, 2, or 3, and semistability implies stability, we express the invariants in terms of known modular forms. We prove a combinato-rial formula for the invariants when k = 2 in the presence of the strictly semistable sheaves, and verify the BPS integrality conjecture of [JS11] in some cases. 1