Commutative $B{V}_{\infty }$ algebras, their morphisms and $\frac{\infty }{2}$-variation of Hodge structures

Abstract

We study morphisms between commutative $B{V}_{\infty }$ algebras and show that, under suitable additional assumptions, a quasi-isomorphism of commutative $B{V}_{\infty }$ algebras induces an identification of $\frac{\infty }{2}$-variations of Hodge structures with polarizations, and consequently of Frobenius manifolds. An explicit example arising from singularity theory is provided to illustrate the result.

arXiv comment14 pages. Comments welcome