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arXiv · 2601.00132

Elements of Saito theory via Batalin--Vilkovisky algebras

Alexey Basalaev
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Abstract

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.

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Alexey Basalaev. 2025-12-31. Elements of Saito theory via Batalin--Vilkovisky algebras. https://arxiv.org/abs/2601.00132

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