Schrödinger equations, deformation theory and $t{t}^{\ast }$-geometry

Abstract

This is the first of a series of papers to construct the deformation theory of the form Schrödinger equation, which is related to a section-bundle system $(M,g,f)$, where $(M,g)$ is a noncompact complete Kähler manifold with bounded geometry and $f$ is a holomorphic function defined on $M$. This work is also the first step attempting to understand the whole Landau-Ginzburg B-model including the higher genus invariants. Our work is mainly based on the pioneer work of Cecotti, Cecotti and Vafa \cite{Ce1,Ce2,CV}.

Deformation theory, Landau-Ginzburg B model, 114 pages

References in corpus (8)

• A Generalized Construction of Mirror Manifolds
• Tautological relations and the r-spin Witten conjecture
• Geometry and Integrability of Topological-Antitopological Fusion
• FJRW rings and Landau-Ginzburg Mirror Symmetry
• Landau-Ginzburg/Calabi-Yau correspondence for quintic three-folds via symplectic transformations
• Quantum BCOV theory on Calabi-Yau manifolds and the higher genus B-model
• A-twisted Landau-Ginzburg models
• tt*-geometry in quantum cohomology

Cited by in corpus (8)

• E_1-degeneration of the irregular Hodge filtration (with an appendix by Morihiko Saito)
• Primitive forms via polyvector fields
• A twisted ${\bar{\partial }}_f$-Neumann problem and Toeplitz $n$-tuples from singularity theory
• Virtual Residue and an integral formalism
• On the L2-Hodge theory of Landau-Ginzburg models
• $t{t}^{\ast }$ Geometry, Singularity Torsion and Anomaly Formulas
• HOMFLY polynomial from a generalized Yang-Yang function
• Witten Deformation on Non-compact Manifold: Heat Kernel Expansion and Local Index Theorem