English

Vector flows and the analytic moduli of singular plane branches

Algebraic Geometry 2019-03-21 v7

Abstract

We provide a geometric elementary proof of the fact that an analytic plane branch is analytically equivalent to one whose terms corresponding to contacts with holomorphic one-forms -- except for Zariski's λ\lambda-invariant -- are zero (so called "short parametrizations"). This is the main step missed by Zariski in his attempt to solve the moduli problem.

Keywords

Cite

@article{arxiv.1704.05265,
  title  = {Vector flows and the analytic moduli of singular plane branches},
  author = {Pedro Fortuny Ayuso},
  journal= {arXiv preprint arXiv:1704.05265},
  year   = {2019}
}

Comments

Much improved proof with very detailed sections on contacts, Taylor expansions and n-th roots

R2 v1 2026-06-22T19:19:54.127Z