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

我们提出在全纯曲线的导出模空间上利用Quillen行列式研究Witten亏格。我们希望对Witten亏格的解析解释的最新进展的这种更几何的方法更适合于应用。所提出的策略利用高等细菌来研究派生的模空间上的Quillen行列式，由此产生了Witten亏格。然后在这个框架中勾画了Calabi-Yau流形和Hyperk\“Ahler度量在障碍中的潜在应用。

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.