English

Families of proper holomorphic maps

Complex Variables 2026-02-04 v1

Abstract

Given a smooth, open, oriented surface XX endowed with a family of complex structures {Jb}bB\{J_b\}_{b\in B} depending continuously on the parameter bb in a metrisable space BB, we construct a continuous family of proper holomorphic maps Fb:(X,Jb)C2F_{b}:(X,J_b)\to\mathbb C^{2}, bBb\in B.

Keywords

Cite

@article{arxiv.2511.11188,
  title  = {Families of proper holomorphic maps},
  author = {Barbara Drinovec Drnovsek and Jure Kalisnik},
  journal= {arXiv preprint arXiv:2511.11188},
  year   = {2026}
}