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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.14077 |
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| _version_ | 1866915938915319808 |
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| author | Proserpio, Alessandro Strachan, Ian A. B. |
| author_facet | Proserpio, Alessandro Strachan, Ian A. B. |
| contents | The idea of a $\bigvee$-system was introduced by Veselov in the study of rational solutions of the WDVV equations of associativity. These are algebraic/geometric conditions on the set of covectors that appear in rational solutions to the WDVV equations. Here, this idea is generalized to open WDVV equations, which are an additional set of PDEs originating from open Gromow-Witten Theory. We develop -- for rank-one extensions -- algebraic/geometric conditions on the covectors that supplement the $\bigvee$-system to give rational solutions to the open WDVV equations. Examples, and the relation to superpotentials and to Dubrovin almost-duality, are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14077 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Open WDVV equations and $\bigvee$-systems Proserpio, Alessandro Strachan, Ian A. B. Mathematical Physics Representation Theory Exactly Solvable and Integrable Systems 53D45 (Primary), 20F55, 35C05, 58J60 (Secondary) The idea of a $\bigvee$-system was introduced by Veselov in the study of rational solutions of the WDVV equations of associativity. These are algebraic/geometric conditions on the set of covectors that appear in rational solutions to the WDVV equations. Here, this idea is generalized to open WDVV equations, which are an additional set of PDEs originating from open Gromow-Witten Theory. We develop -- for rank-one extensions -- algebraic/geometric conditions on the covectors that supplement the $\bigvee$-system to give rational solutions to the open WDVV equations. Examples, and the relation to superpotentials and to Dubrovin almost-duality, are given. |
| title | Open WDVV equations and $\bigvee$-systems |
| topic | Mathematical Physics Representation Theory Exactly Solvable and Integrable Systems 53D45 (Primary), 20F55, 35C05, 58J60 (Secondary) |
| url | https://arxiv.org/abs/2604.14077 |