$t{t}^{\ast }$ Geometry, Singularity Torsion and Anomaly Formulas

Abstract

This paper is concerned with the Schrödinger operators ${\Delta }_{f_0}$ and ${\Delta }_f$ attached to a pair $({\mathbb{C}}^n,f_0)$ and its deformation $({\mathbb{C}}^n,f)$, where $f_0$ is a non-degenerate and quasi-homogeneous polynomial on ${\mathbb{C}}^n$ and $f$ is its relevant or marginal deformation. We give the $t{t}^{\ast }$ geometry structure on the Hodge bundle associated to ${\Delta }_f$, which describes the genus 0 anomaly. Next we study the corresponding singularity torsion type invariants and give the anomaly formulas for the 2nd torsion type invariant.

References in corpus (2)

• Schrödinger equations, deformation theory and $t{t}^{\ast }$-geometry
• Torsion type invariants of singularities