Residue polytopes
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913551019409408 |
|---|---|
| author | Amini, Omid Esteves, Eduardo Garcez, Eduardo |
| author_facet | Amini, Omid Esteves, Eduardo Garcez, Eduardo |
| contents | A level graph is the data of a pair $(G,π)$ consisting of a finite graph $G$ and an ordered partition $π$ on the set of vertices of $G$. To each level graph on $n$ vertices we associate a polytope in $\mathbb R^n$ called its residue polytope. We show that residue polytopes are compatible with each other in the sense that if $π'$ is a coarsening of $π$, then the polytope associated to $(G,π)$ is a face of the one associated to $(G,π')$. Moreover, they form all the faces of the residue polytope of $G$, defined as the polytope associated to the level graph with the trivial ordered partition. The results are used in a companion work to describe limits of spaces of Abelian differentials on families of Riemann surfaces approaching a stable Riemann surface on the boundary of the moduli space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_13554 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Residue polytopes Amini, Omid Esteves, Eduardo Garcez, Eduardo Combinatorics Algebraic Geometry A level graph is the data of a pair $(G,π)$ consisting of a finite graph $G$ and an ordered partition $π$ on the set of vertices of $G$. To each level graph on $n$ vertices we associate a polytope in $\mathbb R^n$ called its residue polytope. We show that residue polytopes are compatible with each other in the sense that if $π'$ is a coarsening of $π$, then the polytope associated to $(G,π)$ is a face of the one associated to $(G,π')$. Moreover, they form all the faces of the residue polytope of $G$, defined as the polytope associated to the level graph with the trivial ordered partition. The results are used in a companion work to describe limits of spaces of Abelian differentials on families of Riemann surfaces approaching a stable Riemann surface on the boundary of the moduli space. |
| title | Residue polytopes |
| topic | Combinatorics Algebraic Geometry |
| url | https://arxiv.org/abs/2410.13554 |