Palais leaf-space manifolds and surfaces carrying holomorphic flows
Ana Cristina Ferreira, Julio C. Rebelo, Helena Reis
TL;DR
This paper constructs complex surfaces with complete holomorphic vector fields exhibiting new dynamical behaviors, expanding understanding beyond algebraic cases and starting from special singularities.
Contribution
It introduces novel examples of complete holomorphic vector fields on complex surfaces derived from specific singularities, extending the scope beyond algebraic geometry.
Findings
Examples of complete vector fields with new dynamical phenomena
Construction of complex surfaces from special singularities
Extension beyond algebraic settings
Abstract
Starting from some remarkable singularities of holomorphic vector fields, we construct (open) complex surfaces over which the singularities in question are realized by complete vector fields. Our constructions lead to manifolds and vector fields beyond the algebraic setting and provide examples of complete vector fields with some new dynamical phenomena.
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