English

Elements of Saito theory via Batalin--Vilkovisky algebras

Algebraic Geometry 2026-01-05 v1

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.

Keywords

Cite

@article{arxiv.2601.00132,
  title  = {Elements of Saito theory via Batalin--Vilkovisky algebras},
  author = {Alexey Basalaev},
  journal= {arXiv preprint arXiv:2601.00132},
  year   = {2026}
}