Stabilization of Kac polynomials along root strings
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909831230652416 |
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| author | Zveryk, Vladyslav |
| author_facet | Zveryk, Vladyslav |
| contents | We study the stabilization behavior of cohomology groups associated with moduli spaces of quiver representations for a fixed quiver $Q$. Under mild conditions on a dimension vector $δ$, we show that the dimensions of these cohomology groups stabilize when a sufficiently large multiple of $δ$ is added. We derive explicit formulas for the stabilized dimensions and, in particular, obtain stabilization of the coefficients of Kac polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stabilization of Kac polynomials along root strings Zveryk, Vladyslav Representation Theory Algebraic Geometry We study the stabilization behavior of cohomology groups associated with moduli spaces of quiver representations for a fixed quiver $Q$. Under mild conditions on a dimension vector $δ$, we show that the dimensions of these cohomology groups stabilize when a sufficiently large multiple of $δ$ is added. We derive explicit formulas for the stabilized dimensions and, in particular, obtain stabilization of the coefficients of Kac polynomials. |
| title | Stabilization of Kac polynomials along root strings |
| topic | Representation Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2505.05439 |