Algebraic models of local period maps and Yukawa algebras

2015/06/30 by Ruggero Bandiera, Marco Manetti
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Cohomology #Computer science #De Rham cohomology #Equivariant cohomology #Geometry #Geometry and complex manifolds #Grassmannian #Hodge theory #Homotopy and Cohomology in Algebraic Topology #Interpretation (philosophy) #Manifold (fluid mechanics) #Mathematics #Particle physics #Period (music) #Physics #Product (mathematics) #Pure mathematics #Yukawa potential #math.AG #math.QA

paper · pdf · doi:10.1007/s11005-018-1064-1

published as Letters in Mathematical Physics 108, 2055-2097 (2018) · to appear in Letters in Mathematical Physics

arxiv created 2018/02/07 · openalex publication_date 2018/02/17 · arxiv updated 2018/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We describe some L-infinity model for the local period map of a compact Kaehler manifold. Applications include the study of deformations with associated variation of Hodge structure constrained by certain closed strata of the Grassmannian of the de Rham cohomology. As a byproduct we obtain an interpretation in the framework of deformation theory of the Yukawa coupling.

Citations

• Differential Graded Lie Algebras and Deformations of Holomorphic Maps
• Deformation theory and rational homotopy type
• Infinitesimal Methods in Hodge Theory
• Differential Analysis on Complex Manifolds