Images and singularity subsets of pseudoholomorphic maps

TL;DR

This paper investigates the properties of images and singularity subsets of pseudoholomorphic maps, establishing conditions under which these sets are pseudoholomorphic subvarieties or subsets, especially in four-dimensional cases.

Contribution

It proves that the image of a proper pseudoholomorphic map is a pseudoholomorphic subvariety and that the singularity subset is pseudoholomorphic when the domain is four-dimensional.

Findings

Image of proper pseudoholomorphic maps in 4D is a subvariety

Singularity subset is pseudoholomorphic in 4D

Results extend understanding of pseudoholomorphic map structures

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.