The unique tangent cone property for weakly holomorphic maps into projective algebraic varieties

Abstract

We establish the uniqueness of tangent maps for general weakly holomorphic and locally approximable maps from an arbitrary almost complex manifold into projective algebraic varieties. As a by-product of the approach and the techniques developed, we also obtain the unique tangent cone property for a special class of nonrectifiable positive pseudoholomorphic cycles. This approach also gives a new proof of the main result by Bellettini on the uniqueness of tangent cones for positive integral $(p,p)$-cycles in arbitrary almost complex manifolds.