First-order deformation tensors over compact Riemann surfaces

The moduli problem for germs of codimension one, smooth embeddings of a compact Riemann surface of general type with a fixed positive line bundle as the normal bundle is studied. The formal tangent space of the moduli space of deformation tensors at the origin and first order extensible CR-deformations on the circle bundle are found, then we establish a one-to-one correspondence between these objects.