Generic Irreducibility of Bloch Varieties for Periodic Graph Operators
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909009905188864 |
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| author | Faust, Matthew Liu, Wencai |
| author_facet | Faust, Matthew Liu, Wencai |
| contents | We give a complete characterization of generic irreducibility for dispersion polynomials and Bloch varieties of periodic graph operators. More precisely, we prove that for a generic choice of edge weights and potentials, the dispersion polynomial/Bloch variety of a nontrivial periodic graph is irreducible if and only if the quotient graph is connected.
Our proof uses a strong dichotomy for parameterized Laurent polynomials: reducibility either occurs for every parameter or fails on a nonempty Zariski-open set. After establishing this dichotomy, we reduce the problem to minimally connected periodic graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01212 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generic Irreducibility of Bloch Varieties for Periodic Graph Operators Faust, Matthew Liu, Wencai Spectral Theory Mathematical Physics Algebraic Geometry Combinatorics 14M25, 47A75, 81Q10 We give a complete characterization of generic irreducibility for dispersion polynomials and Bloch varieties of periodic graph operators. More precisely, we prove that for a generic choice of edge weights and potentials, the dispersion polynomial/Bloch variety of a nontrivial periodic graph is irreducible if and only if the quotient graph is connected. Our proof uses a strong dichotomy for parameterized Laurent polynomials: reducibility either occurs for every parameter or fails on a nonempty Zariski-open set. After establishing this dichotomy, we reduce the problem to minimally connected periodic graphs. |
| title | Generic Irreducibility of Bloch Varieties for Periodic Graph Operators |
| topic | Spectral Theory Mathematical Physics Algebraic Geometry Combinatorics 14M25, 47A75, 81Q10 |
| url | https://arxiv.org/abs/2605.01212 |