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We derive the partition functions of the Schwarz-type four-dimensionaltopological half-flat 2-form gravity model on K3-surface or T^4 up to on-shellone-loop corrections. In this model the bosonic moduli spaces describe anequivalent class of a trio of the Einstein-K\"ahler forms (the hyperk\"ahlerforms). The integrand of the partition function is represented by the productof some $\bar \partial$-torsions.Comment: 10 pages, LaTex, Replacement: the conclusion is correcte

The Partition Function in the Four-Dimensional Schwarz-Type Topological Half-Flat Two-Form Gravity