%0 Journal Article
%T Boundaries of Positive Holomorphic Chains and the Relative Hodge Question
%A F. Reese Harvey
%A H. Blaine Lawson Jr
%J Mathematics
%D 2006
%I arXiv
%X We characterize the boundaries of positive holomorphic chains (with both compact and non-compact support) in an arbitrary complex manifold. We then consider a compact oriented real submanifold of dimension 2p-1 in a compact Kahler manifold X and address the question of which relative homology classes in H_{2p}(X,M;Z) are represented by positive holomorphic chains. Specifically, we define what it means for a class u in H_{2p}(X,M;Z) to be of type (p,p) and positive. It is then shown that u has these properties if and only if u = [T+S] where T is a positive holomorphic chain with dT = du and S is a positive (p,p)-current with dS = 0.
%U http://arxiv.org/abs/math/0610533v2