Images and singularity subsets of pseudoholomorphic maps

2022/12/07 by Weiyi Zhang, Zhang, Weiyi
Mathematics · #Analytic and geometric function theory #Artificial intelligence #Complex Variables (math.CV) #Computer science #Differential Geometry (math.DG) #Dimension (graph theory) #Domain (mathematical analysis) #FOS: Mathematics #Holomorphic and Operator Theory #Image (mathematics) #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Pure mathematics #Singularity #Statistics #Subvariety

paper · pdf · doi:10.48550/arxiv.2212.03982

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2022/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08

Abstract

We study the image and the singularity subset of a general pseudoholomorphic map. We show that the image of a proper pseudoholomorphic map is a pseudoholomorphic subvariety when the dimension of either the domain or target is four. We also prove that the singularity subset of a pseudoholomorphic map is pseudoholomorphic when the domain has dimension four.

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