Smoothing of multiple structures on embedded Enriques manifolds

We show that given an embedding of Enriques manifold index d in a large enough projective space, there will exist embedded multiple structures with conormal bundle isomorphic to the trace zero module universal covering map, cover being either hyperkähler or Calabi–Yau manifold. then these (also known as d-ropes) can be smoothed smooth manifolds respectively. Hence we obtain flat family (or Calabi–Yau) same space which degenerates d-rope structure on d. The above shows are points Hilbert scheme containing fibres family. they when $$d=2$$ .