Braid monodromy for a trinomial algebraic equation by means of Mellin-Barnes integral representations
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913526465953792 |
|---|---|
| author | Kocar, Mutlu Tanabe, Susumu |
| author_facet | Kocar, Mutlu Tanabe, Susumu |
| contents | We establish a braid monodromy representation of functions satisfying an algebraic equation containing three terms (trinomial equation). We follow global analytic continuation of the roots to a trinomial algebraic equation that are expressed by Mellin-Barnes integral representations. We depict braids that arise from the monodromy around all branching points. The global braid monodromy is described in terms of rational twists of strands that yield a classical Artin braid representation of algebraic functions. As a corollary, we get a precise description of the Galois group of a trinomial algebraic equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16459 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Braid monodromy for a trinomial algebraic equation by means of Mellin-Barnes integral representations Kocar, Mutlu Tanabe, Susumu Algebraic Geometry Classical Analysis and ODEs Complex Variables Geometric Topology 14H05, 20F36, 33C20 We establish a braid monodromy representation of functions satisfying an algebraic equation containing three terms (trinomial equation). We follow global analytic continuation of the roots to a trinomial algebraic equation that are expressed by Mellin-Barnes integral representations. We depict braids that arise from the monodromy around all branching points. The global braid monodromy is described in terms of rational twists of strands that yield a classical Artin braid representation of algebraic functions. As a corollary, we get a precise description of the Galois group of a trinomial algebraic equation. |
| title | Braid monodromy for a trinomial algebraic equation by means of Mellin-Barnes integral representations |
| topic | Algebraic Geometry Classical Analysis and ODEs Complex Variables Geometric Topology 14H05, 20F36, 33C20 |
| url | https://arxiv.org/abs/2409.16459 |