The partition function in the four-dimensional Schwarz-type topological half-flat two-form gravity

We examine the partition functions and the renormalization of the Schwarz-type four-dimensional topological half-flat 2-form gravity model on K3-surface or T^4 up to on-shell one-loop corrections. In this model the bosonic moduli spaces describe an equivalent class of a trio of the Einstein-K\"ahler forms ( the hyperk\"ahler forms )