Skip to Main content Skip to Navigation
Journal articles

Non density of stability for holomorphic mappings on P^k

Abstract : A well-known theorem due to Mañé-Sad-Sullivan and Lyubich asserts that J-stable maps are dense in any holomorphic family of rational maps in dimension 1. In this paper we show that the corresponding result fails in higher dimension. More precisely, we construct open subsets in the bifurcation locus in the space of holomorphic mappings of degree d of P^k (C) for every d ≥ 2 and k ≥ 2.
Document type :
Journal articles
Complete list of metadatas

Cited literature [20 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01376983
Contributor : Romain Dujardin <>
Submitted on : Monday, October 24, 2016 - 4:00:13 PM
Last modification on : Saturday, March 28, 2020 - 2:18:52 AM

Files

robust.pdf
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution 4.0 International License

Identifiers

  • HAL Id : hal-01376983, version 2
  • ARXIV : 1610.01785

Citation

Romain Dujardin. Non density of stability for holomorphic mappings on P^k. Journal de l'Ecole Polytechnique, Ecole Polytechnique, 2017, 4, pp.813-843. ⟨hal-01376983v2⟩

Share

Metrics

Record views

313

Files downloads

110