Criteria for holomorphic completeness. II

It is proved that a complex space X of finite dimension d is holomorphically complete if and only if the following conditions hold: 1) for an arbitrary point x(0) is an element of X there exist analytic sets M-n subset of...subset of M-1 subset of M-0 = X and holomorphic functions f(i) is an element of Gamma (Mi-1; OMi-1), i = 1,...n, such that M-i = (x is an element of Mi-1 : f(i)(x) = 0), and O-Mi = OMi-1/f(i)O(1m-1) \ M-i for each i = 1,..., n, and x(0) is an isolated point in M-n; 2) H-k(X; O-X) = 0 for k = 1,..., d-1.