Quivers, Flow Trees, and Log Curves
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866908556882608128 |
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| author | Argüz, Hülya Bousseau, Pierrick |
| author_facet | Argüz, Hülya Bousseau, Pierrick |
| contents | Donaldson-Thomas (DT) invariants of a quiver with potential can be expressed in terms of simpler attractor DT invariants by a universal formula. The coefficients in this formula are calculated combinatorially using attractor flow trees. In this paper, we prove that these coefficients are genus 0 log Gromov--Witten invariants of $d$-dimensional toric varieties, where $d$ is the number of vertices of the quiver. This result follows from a log-tropical correspondence theorem which relates $(d-2)$-dimensional families of tropical curves obtained as universal deformations of attractor flow trees, and rational log curves in toric varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_02068 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quivers, Flow Trees, and Log Curves Argüz, Hülya Bousseau, Pierrick Algebraic Geometry High Energy Physics - Theory Representation Theory Symplectic Geometry Donaldson-Thomas (DT) invariants of a quiver with potential can be expressed in terms of simpler attractor DT invariants by a universal formula. The coefficients in this formula are calculated combinatorially using attractor flow trees. In this paper, we prove that these coefficients are genus 0 log Gromov--Witten invariants of $d$-dimensional toric varieties, where $d$ is the number of vertices of the quiver. This result follows from a log-tropical correspondence theorem which relates $(d-2)$-dimensional families of tropical curves obtained as universal deformations of attractor flow trees, and rational log curves in toric varieties. |
| title | Quivers, Flow Trees, and Log Curves |
| topic | Algebraic Geometry High Energy Physics - Theory Representation Theory Symplectic Geometry |
| url | https://arxiv.org/abs/2302.02068 |