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<p>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.</p>

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On the Geometry of Holomorphic Curves and Complex Surface

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月2日

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  • Amanda Dias Falqueto,
  • Farid Tari

摘要

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.