Critical groups in harmonic abelian quotients
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866917770775494656 |
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| author | Vetluzhskikh, Mariia Zakharov, Dmitry |
| author_facet | Vetluzhskikh, Mariia Zakharov, Dmitry |
| contents | A harmonic cover of graphs $p:\widetilde{X}\to X$ induces a surjective pushforward morphism $p_*:\operatorname{Jac}(\widetilde{X})\to \operatorname{Jac}(X)$ on the critical groups. In the case when $p$ is Galois with abelian Galois group, we compute the order of the kernel of $p_*$, and hence the relationship between the numbers of spanning trees of $\widetilde{X}$ and $X$, in terms of Zaslavsky's bias matroid associated to the cover $p:\widetilde{X}\to X$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04629 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Critical groups in harmonic abelian quotients Vetluzhskikh, Mariia Zakharov, Dmitry Combinatorics Algebraic Geometry 05C31, 14H40 A harmonic cover of graphs $p:\widetilde{X}\to X$ induces a surjective pushforward morphism $p_*:\operatorname{Jac}(\widetilde{X})\to \operatorname{Jac}(X)$ on the critical groups. In the case when $p$ is Galois with abelian Galois group, we compute the order of the kernel of $p_*$, and hence the relationship between the numbers of spanning trees of $\widetilde{X}$ and $X$, in terms of Zaslavsky's bias matroid associated to the cover $p:\widetilde{X}\to X$. |
| title | Critical groups in harmonic abelian quotients |
| topic | Combinatorics Algebraic Geometry 05C31, 14H40 |
| url | https://arxiv.org/abs/2409.04629 |