On the truncated defect relation for holomorphic curves

Abstract

For a transcendental holomorphic curve and a subset of C^{n + 1} − {0} in subgeneral position, we consider the truncated defect relation by using a generalization of Nochka weight function introduced in [12] and its supplement in Section 3. When it is not extremal, we estimate the sum of defects and when it is extremal, we investigate the number of vectors each defect of which is equal to 1 or the structure of vectors each defect of which is positive.