Tangent cones to positive-(1,1) De Rham currents

Details Tangent cones to positive-(1,1) De Rham currents Tangent cones to positive-(1,1) De Rham currents

2011-06-23

arxiv.org/abs/1106.4776v1

Mathematics

Analysis of PDEs

37 pages, 2 figures

Scientific paper

We consider positive-(1,1) De Rham currents in arbitrary almost complex manifolds and prove the uniqueness of the tangent cone at any point where the density does not have a jump with respect to all of its values in a neighbourhood. Without this assumption, counterexamples to the uniqueness of tangent cones can be produced already in C^n, hence our result is optimal. The key idea is an implementation, for currents in an almost complex setting, of the classical blow up of curves in algebraic or symplectic geometry. Unlike the classical approach in C^n, we cannot rely on plurisubharmonic potentials.

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