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

2015/03/31 by Takahashi, Atsushi
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.09099

Abstract

It is one of the most important problems in mirror symmetry to obtain functorially Frobenius manifolds from smooth compact Calabi-Yau A_∞-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.

Related

• Calabi-Yau algebras
• DGBV Algebras and Mirror Symmetry
• Deformed Calabi-Yau Completions
• Smooth projective Calabi-Yau complete intersections and algorithms for their Frobenius manifolds and higher residue pairings
• A Construction of Formal Frobenius Manifold from Deformation of Complex Structure