Elements of Saito theory via Batalin--Vilkovisky algebras
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909979735228416 |
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| author | Basalaev, Alexey |
| author_facet | Basalaev, Alexey |
| contents | Saito theory associates to a quasihomogeneous isolated singularity the structure of a Dubrovin--Frobenius manifold. This structure is not unique, depending on the special choice of a primitive form or, equivalently, a good basis.
We study primitive forms and respective Dubrovin--Frobenius manifolds via BV-algebras. In particular, we give recursive formulae for the primitive form of K. Saito and the R-matrix of Givental using BV-algebra computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_00132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elements of Saito theory via Batalin--Vilkovisky algebras Basalaev, Alexey Algebraic Geometry Saito theory associates to a quasihomogeneous isolated singularity the structure of a Dubrovin--Frobenius manifold. This structure is not unique, depending on the special choice of a primitive form or, equivalently, a good basis. We study primitive forms and respective Dubrovin--Frobenius manifolds via BV-algebras. In particular, we give recursive formulae for the primitive form of K. Saito and the R-matrix of Givental using BV-algebra computations. |
| title | Elements of Saito theory via Batalin--Vilkovisky algebras |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.00132 |