WEAKLY HOLOMORPHIC FUNCTIONS ON COMPLETE INTERSECTIONS, AND THEIR HOLOMORPHIC EXTENSION

The properties of weakly holomorphic functions on analytic sets which are complete intersections are investigated: universal denominators are determined for a system of equations defining the analytic set ; a (residual) current is constructed such that it is -closed if and only if the weakly holomorphic function can be locally extended from ; and integral representations for weakly holomorphic functions are given. These results are applied to the problem of lowering the order of poles of rational differential 2-forms in .Bibliography: 20 titles.