Interactions of Derived Moduli Spaces and Gerbes with Elliptic Genera in Complex Geometry

点击翻译按钮获取中文摘要

We propose the investigation of the Witten genus using the Quillen determinant on the derived moduli space of holomorphic curves. We hope this more geometric approach to the recent advances towards an analytic interpretation of the Witten genus is better suited for applications. The suggested strategy utilizes higher gerbes for the study of the Quillen determinant on the derived moduli space, from which the Witten genus arises. A potential application to obstructions for Calabi--Yau manifolds and hyperk\"ahler metrics is then sketched in this framework.