Complex sentence: If the d-bar operator can be shown to be transverse to the zero-section, this moduli space will be a smooth manifold, which plays a fundamental role in the theory of pseudoholomorphic curves and Gromov-Witten theory.
Split into simpler sentences: If the d-bar operator can be shown to be transverse to the zero-section, this moduli space will be a smooth manifold. These considerations play a fundamental role in the theory of pseudoholomorphic curves and Gromov-Witten theory.