2013/11/07 by Changzheng Li, Si Li, Li, Changzheng +3
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.AG #math.CV #math.QA
paper · pdf · doi:10.48550/arxiv.1311.1659
61 pages, remarks added. Mistake on the analyticity in the previous version is corrected. Details on the correspondence for formal primitive forms added
arxiv created 2014/02/03 · arxiv updated 2014/02/04
We develop a complex differential geometric approach to the theory of higher residues and primitive forms from the viewpoint of Kodaira-Spencer gauge theory, unifying the semi-infinite period maps for Calabi-Yau models and Landau-Ginzburg models. We give an explicit perturbative construction of primitive forms with respect to opposite filtrations and primitive elements. This leads to a concrete algorithm to compute the Taylor expansions of primitive forms as well as the description of their moduli space for all weighted homogenous cases. As an example, we present unknown perturbative expressions for the primitive form of E12 singularity and illustrate its application to Landau-Ginzburg mirror symmetry with FJRW-theory.