Tangent cones to positive-(1,1) De Rham currents
We consider positive-( ) 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 neighborhood. Without this assumption, counterexamples to the uniqueness of tangent...
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| Published in | Journal für die reine und angewandte Mathematik Vol. 2015; no. 709; pp. 15 - 50 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
De Gruyter
01.12.2015
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| Online Access | Get full text |
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| Summary: | We consider positive-(
) 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 neighborhood. Without this assumption, counterexamples to the uniqueness of tangent cones can be produced already in ℂ
, 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
, we cannot rely on plurisubharmonic potentials. |
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| ISSN: | 0075-4102 1435-5345 |
| DOI: | 10.1515/crelle-2013-0082 |