On reflection maps from the $n$-space to the $n+1$-space
Abstract
We consider some problems about a reflected graph map germ f from (\mathbb{C}^{n},0) to (\mathbb{C}^{n+1},0) . A reflected graph map is a particular case of a reflection map, which is defined using an embedding of \mathbb{C}^{n} in \mathbb{C}^{p} and then applying the action of a reflection group G on \mathbb{C}^{p} . We present a description of the presentation matrix of f_{*}\mathcal{O}_{n} as an \mathcal{O}_{n+1} -module via f in terms of the action of the associated reflection group G . We also give a description for a defining equation of the image of f in terms of the action of G . Finally, we provide an upper (and also a lower) bound for the multiplicity of the image of f and some applications.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Commutative Algebra and Its Applications
Geometry and complex manifolds
Publication details
- Journal / source
- Revista Matemática Iberoamericana
- Volume
- 42
- Issue
- 2
- Pages
- 441–476
- Publication date
- 20 January 2026
- Language
- EN