On Deformations of Generalized Complex Structures: the Generalized Calabi-Yau Case

TL;DR

This paper proves that the moduli space of generalized complex structures on twisted generalized Calabi-Yau manifolds is smooth and unobstructed, extending classical deformation results to a broader geometric context.

Contribution

It establishes an analog of the Tian-Todorov theorem for twisted generalized Calabi-Yau manifolds, showing the unobstructedness and smoothness of their moduli space.

Findings

Moduli space of structures is unobstructed and smooth

Constructed the extended moduli space with Frobenius structure

Discussed physical implications of the geometric results

Abstract

We prove an analog of the Tian-Todorov theorem for twisted generalized Calabi-Yau manifolds; namely, we show that the moduli space of generalized complex structures on a compact twisted generalized Calabi-Yau manifold is unobstructed and smooth. We also construct the extended moduli space and study its Frobenius structure. The physical implications are also discussed.