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March 4, 2026Open Access

On the Geometry of Holomorphic Curves and Complex Surface

AFAmanda Dias FalquetoBrazilian Society of Computational and Applied Mathematics FTFarid Tari

Key Points

The aim is to explore the geometry of holomorphic curves and complex surfaces using singularity theory.
Investigated the geometry of holomorphic curves and complex surfaces.
Applied singularity theory techniques to assess geometry.
Utilized a holomorphic metric to measure contact between curves and surfaces.
Demonstrated that families of functions measuring contact are holomorphic.
Identified invariant properties under translations and complex rotations.

Abstract

Abstract We investigate the geometry of holomorphic curves and complex surfaces from a singularity theory viewpoint. We show that with the choice of the holomorphic metric, the families of functions and mappings that measure the contact between curves or surfaces with model objects are holomorphic. This allows the application of singularity theory techniques to pick up the geometry that is invariant under translations and complex rotations.

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