Transversality for Holomorphic Supercurves

Holomorphic supercurves are motivated by supergeometry as a natural generalisation of holomorphic curves. In the characterisation as a tuple consisting of a holomorphic curve and certain sections, we consider a slightly weaker form of the defining equations. This is such that, upon perturbing them to depend on a connection, the corresponding linearised operator is generically surjective. By this transversality result, we show that the resulting moduli spaces are oriented finite dimensional smooth manifolds. Finally, we examine how they depend on the choice of generic data. A companion article establishes compactness results in this context.