The Geometry of Locally Bounded Rational Functions
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909347305488384 |
|---|---|
| author | Delage, Victor Fichou, Goulwen Patel, Aftab |
| author_facet | Delage, Victor Fichou, Goulwen Patel, Aftab |
| contents | This paper develops the geometry of locally bounded rational functions on non-singular real algebraic varieties. First various basic geometric and algebraic results regarding these functions are established in any dimension, culminating with a version of Łojasiewicz's inequality. The geometry is further developed for the case of dimension 2, where it can be shown that there exist many of the usual correspondences between the algebra and geometry of these functions that one expects from complex algebraic geometry and from other classes of functions in real algebraic geometry such as regulous functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04232 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Geometry of Locally Bounded Rational Functions Delage, Victor Fichou, Goulwen Patel, Aftab Algebraic Geometry 14P99, 14E05, 14F17, 26C15 This paper develops the geometry of locally bounded rational functions on non-singular real algebraic varieties. First various basic geometric and algebraic results regarding these functions are established in any dimension, culminating with a version of Łojasiewicz's inequality. The geometry is further developed for the case of dimension 2, where it can be shown that there exist many of the usual correspondences between the algebra and geometry of these functions that one expects from complex algebraic geometry and from other classes of functions in real algebraic geometry such as regulous functions. |
| title | The Geometry of Locally Bounded Rational Functions |
| topic | Algebraic Geometry 14P99, 14E05, 14F17, 26C15 |
| url | https://arxiv.org/abs/2409.04232 |