On germs of mappings $\mathbb C^2\to\mathbb C^2$
Algebraic Geometry
2025-12-10 v1
Authors:
S. Yu. Orevkov
Abstract
We describe germs of mappings (C2,0)→(C2,0) ramified along a germ of irreducible curve whose image is of the form xp=yq.
Cite
@article{arxiv.2512.07986,
title = {On germs of mappings $\mathbb C^2\to\mathbb C^2$},
author = {S. Yu. Orevkov},
journal= {arXiv preprint arXiv:2512.07986},
year = {2025}
}
Related papers
View all related →
Algebraic Geometry · Mathematics
On irreducible germs of generic morphisms
Vik. S. Kulikov
2025-03-11
Algebraic Geometry · Mathematics
Images of maps from $(\mathbb{C}^2,0)$ to $(\mathbb{C}^n,0)$
Helge Møller Pedersen
2025-10-31
Algebraic Geometry · Mathematics
The fibers of the ramified Prym map
P. Frediani, J. C. Naranjo, I. Spelta
2021-05-10
Complex Variables · Mathematics
Topology of singular foliation germs in $\mathbb C^2$
David Marín, Jean-François Mattei, Eliane Salem
2023-01-26
Algebraic Geometry · Mathematics
Characterization of curves in $C^{(2)}$
Meritxell Sáez
2015-07-24
Algebraic Geometry · Mathematics
On the topology of the transversal slice of a quasi-homogeneous map germ
Otoniel Nogueira da Silva
2021-07-29
Algebraic Geometry · Mathematics
Number of moduli for an union of smooth curves in (C^2,0)
Yohann Genzmer
2021-06-28
Algebraic Geometry · Mathematics
Cusps in $\mathbb{C}^3$ with prescribed ramification
Ethan Cotterill, Nathan Kaplan, Renata Vieira Costa
2023-10-18
Algebraic Geometry · Mathematics
A note on the ramification of torsion points lying on curves of genus at least two
Damian Rossler
2009-02-25
Complex Variables · Mathematics
Images of analytic map germs, and singular fibrations
Cezar Joiţa, Mihai Tibăr
2020-09-16
Algebraic Geometry · Mathematics
How to Reconstruct a Planar Map From its Branching Curve
Eriola Hoxhaj, Josef Schicho
2023-07-19
Complex Variables · Mathematics
The Saito module and the moduli of a germ of curve in $\left(\mathbb{C}^{2},0\right)$
Yohann Genzmer
2022-04-13
Differential Geometry · Mathematics
Manifolds of mappings for continuum mechanics
Peter W. Michor
2021-11-02
Algebraic Geometry · Mathematics
Families of genus two curves with many elliptic subcovers
Tony Shaska
2012-09-04
Complex Variables · Mathematics
A formula to calculate the invariant $J$ of a quasi-homogeneous map germ
Otoniel Nogueira da Silva
2020-01-13
Complex Variables · Mathematics
Note on Milnor numbers of irreducible germs
Zbigniew Jelonek
2023-01-24
Number Theory · Mathematics
A family of irreducible supersingular representations of $\mathrm{GL}_2(F)$ for some ramified $p$-adic fields
Michael M. Schein
2022-12-26
K-Theory and Homology · Mathematics
Bounding generators for the kernel and cokernel of the tame symbol for curves
Rob de Jeu
2024-10-23
Algebraic Geometry · Mathematics
Toward the classification of threefold extremal contractions with one-dimensional fibers
Shigefumi Mori, Yuri Prokhorov
2025-04-18
Number Theory · Mathematics
Curves of genus two with maps of every degree to a fixed elliptic curve
Everett W. Howe
2026-02-12
Algebraic Geometry · Mathematics
Primitive normal completions of the affine plane II
Pinaki Mondal
2013-07-23
Algebraic Geometry · Mathematics
On the Prym map for cyclic covers of genus two curves
Daniele Agostini
2024-06-19
Algebraic Geometry · Mathematics
Invariant curves for birational surface maps
Jeffrey Diller, Daniel Jackson, Andrew Sommese
2007-05-23
Algebraic Geometry · Mathematics
Second fundamental form of the Prym map in the ramified case
Elisabetta Colombo, Paola Frediani
2019-08-14
Complex Variables · Mathematics
Algebraicity of holomorphic mappings between real algebraic sets in ${\bold C}^n$
M. S. Baouendi, P. Ebenfelt, Linda Preiss Rothschild
2016-09-06