The Unique Tangent Cone Property for Weakly Holomorphic Maps into Projective Algebraic Varieties

Abstract

In the present paper, 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 byproduct of the approach and the techniques developed we also obtain the unique tangent cone property for a special class of non-rectifiable positive pseudo-holomorphic cycles. This approach gives also a new proof of the main result by C. Bellettini on the uniqueness of tangent cones for positive integral $(p,p)$-cycles in arbitrary almost complex manifolds.