English

From Calabi-Yau dg Categories to Frobenius manifolds via Primitive Forms

Algebraic Geometry 2015-06-30 v2

Abstract

It is one of the most important problems in mirror symmetry to obtain functorially Frobenius manifolds from smooth compact Calabi-Yau AA_\infty-categories. This paper gives an approach to this problem based on the theory of primitive forms. Under an assumption on the formality of a certain homotopy algebra, a formal primitive form for a smooth compact Calabi-Yau dg algebra can be constructed, which enable us to have a formal Frobenius manifold.

Keywords

Cite

@article{arxiv.1503.09099,
  title  = {From Calabi-Yau dg Categories to Frobenius manifolds via Primitive Forms},
  author = {Atsushi Takahashi},
  journal= {arXiv preprint arXiv:1503.09099},
  year   = {2015}
}

Comments

22 pages. This article is based on a talk given in Kavli IPMU at the workshop "Primitive forms and related subjects" on February 11th 2014. Corrected typos and minor errors