Rational Endomorphisms of Codimension One Holomorphic Foliations
Federico Lo Bianco (I2M), Jorge Pereira (IMPA), Erwan Rousseau (LM),, Fr\'ed\'eric Touzet (IRMAR)
TL;DR
This paper investigates rational maps that preserve certain complex geometric structures called codimension one foliations on projective manifolds, focusing on their dynamic behavior and properties.
Contribution
It provides a detailed analysis of the structure and dynamics of rational endomorphisms preserving holomorphic foliations, highlighting new classifications and behaviors.
Findings
Identification of conditions for rational maps to preserve foliations
Characterization of transverse dynamics in these maps
New classifications of endomorphisms based on foliation properties
Abstract
In this work, we study dominant rational maps preserving singular holomorphic codimension one foliations on projective manifolds and that exhibit non-trivial transverse dynamics.
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