Pull-back of currents by holomorphic maps

By T. Dinh, N. Sibony. 2006

80 citations recorded by the source corpus.

We define the pull-back operator, associated to a meromorphic transform, on several types of currents. We also give a simple proof to a version of a classical theorem on the extension of currents.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f0658c66a6959e7dc1b1d814f7be3531b0a96702

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In Applied Mathematics

1. Tuyen T. T. Truong
2. N. Sibony
3. T. Dinh
4. Nguyen-Bac Dang
5. De-Qi Zhang
6. Romain Dujardin
7. Keiji Oguiso

In Geometry and Topology

1. N. Sibony
2. T. Dinh
3. Tuyen T. T. Truong
4. Nguyen-Bac Dang
5. De-Qi Zhang
6. Franccois Berteloot
7. Romain Dujardin
8. Vincent Guedj

Citations in the corpus

• Super-potentials of positive closed currents, intersection theory and dynamics (2007, background): “of T′. 63 5.4 Equidistribution problem for endomorphisms Consider a holomorphic map f : Pk → Pk of algebraic degree d ≥ 2. Recall that f∗ acts continuously on positive closed currents of any bidegree [44, 26], see also Paragraphs 5.1 and 5.2. It is well-known that d−n(fn)∗(ω) converge to a positive ”
• Exponential estimates for plurisubharmonic functions and stochastic dynamics (2008, unknown): “C V ] Classification AMS 2000: 32U, 37F. Keywords: Monge-Ampère measure, Green measure, exponential mixing, central limit theorem, large deviations theorem.”
• Density of positive closed currents, a theory of non-generic intersections (2012, background): “unded by a constant times kTkU′, see Chern-LevineNirenberg [5] and Demailly [8]. The lemma follows. Note that the result can be generalized for maps between manifolds of different dimensions, see also [17]. In this paper, we only need the version stated above. Definition 3.13. With the notations as in”
• Relative dynamical degrees of correspondences over a field of arbitrary characteristic (2016, methodology): “(We can also define a strict transform more intrinsically using the graph Γf directly, as in [14].”
• Equidistribution problems of complex dynamics in higher dimension (2016, background): “1, one can show that the obtained current can be extended by 0 to a positive closed (p, p)-current on X, see [29] for details.”