Two semi-coninuity results for the algebraic dimension of compact   complex manifolds
  Using some relative codimension 1 cycle-space method, we give, following the ideas of D. Popovici [P.13], semicontinuity results for the algebraic dimension in a family a compact complex manifolds parametrized by a disc. 
Daniel Barlet (IUF, IECL)
math.CV math.AG