Algebraic models of local period maps and Yukawa algebras

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.

to appear in Letters in Mathematical Physics

References in corpus (5)

• Deformation theory and rational homotopy type
• Lectures on deformations of complex manifolds
• Pre-Lie deformation theory
• L-infinity algebra actions
• A period map for global derived stacks

Cited by in corpus (7)

• Formality conjecture for minimal surfaces of Kodaira dimension 0
• Deformations of Dolbeault cohomology classes
• Derived Differentiable Manifolds
• A local Torelli theorem for log symplectic manifolds
• Deformed Aeppli cohomology: canonical deformations and jumping formulas
• Some remarks on Dupont contraction
• $L_{\infty }$ liftings of semiregularity maps via Chern-Simons classes