Year: 2013
Type: preprint
Abstract: 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 E_12 singularity and illustrate its application to Landau-Ginzburg mirror symmetry with FJRW-theory.
Source: arXiv (Cornell University)
Authors: Li, Changzheng, Li, Si, Saito, Kyoji
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1497438482