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 -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