Generic transversality for simple holomorphic spheres

For a residual set of smooth compatible almost complex structures, all simple J-holomorphic spheres in a specified countable set of spherical classes are regular. The corresponding evaluation maps at marked points are transverse to generic incidence conditions; generic paths give parameterized transversality. The universal linearization can vary the target structure near an injective point of the curve, which removes its cokernel. This assertion concerns simple curves and does not ensure regularity of arbitrary multiple covers.