Geodesic
Weakly holomorphic functions on complete intersections, and their holomorphic extension
Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 421-436

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The properties of weakly holomorphic functions on analytic sets which are complete intersections are investigated: universal denominators are determined for a system of equations $f=0$ defining the analytic set $A$; a (residual) current $hR_f$ is constructed such that it is $\overline\partial$-closed if and only if the weakly holomorphic function $h$ can be locally extended from $A$; 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 $\mathbf C^2$. Bibliography: 20 titles. 
@article{SM_1988_61_2_a9,
     author = {A. K. Tsikh},
     title = {Weakly holomorphic functions on complete intersections, and their holomorphic extension},
     journal = {Sbornik. Mathematics},
     pages = {421--436},
     publisher = {mathdoc},
     volume = {61},
     number = {2},
     year = {1988},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_61_2_a9/}
}
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A. K. Tsikh. Weakly holomorphic functions on complete intersections, and their holomorphic extension. Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 421-436. http://geodesic.mathdoc.fr/item/SM_1988_61_2_a9/