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arXiv · 1710.01473

Super-potentials, densities of currents and number of periodic points for holomorphic maps

Tien-Cuong Dinh·Viet-Anh Nguyen·Duc-Viet Vu
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Abstract

We prove that if a positive closed current is bounded by another one with bounded, continuous or Hoelder continuous super-potentials, then it inherits the same property. There are two different methods to define wedge-products of positive closed currents of arbitrary bi-degree on compact Kaehler manifolds using super-potentials and densities. When the first method applies, we show that the second method also applies and gives the same result. As an application, we obtain a sharp upper bound for the number of isolated periodic points of holomorphic maps on compact Kaehler manifolds whose actions on cohomology are simple. A similar result still holds for a large class of holomorphic correspondences.

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Tien-Cuong Dinh, Viet-Anh Nguyen, Duc-Viet Vu. 2017-10-04. Super-potentials, densities of currents and number of periodic points for holomorphic maps. https://arxiv.org/abs/1710.01473

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