Some Results of Deformations on Compact $H$-twisted Generalized Calabi-Yau Manifolds

TL;DR

This paper proves that deformations of compact H-twisted generalized Calabi-Yau manifolds are unobstructed, establishes L^2 convergence in deformations, and constructs a global canonical family under certain conditions.

Contribution

It introduces formulas related to Hodge theory to demonstrate unobstructed deformations and constructs a global canonical family for generalized Kähler manifolds.

Findings

Deformations are unobstructed under certain conditions.

L^2 convergence is established in a neighborhood.

A global canonical family of deformations is constructed.

Abstract

In this paper, we prove several formulas related to Hodge theory, and using them to prove the deformations of a compact $H$-twisted generalized Calabi-Yau manifold are unobstructed and $L^2$ convergence in a neighborhood in another power series . And if we assume that the deformation is smooth in a fixed neighborhood, and assume the existence of a global canonical family of deformation, we also construct the global canonical family of the deformations of generalized K\"ahler manifolds.