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

复杂几何中导出模空间和Gerbes与椭圆属的相互作用

• 批准号: 376202359
• 负责人: Dr. Markus Upmeier
• 金额: --
• 依托单位: Mathematical Institute
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/376202359?language=en
• 关键词: Interactions; Derived; Moduli; Spaces; Gerbes

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.

提出了利用全纯曲线导模空间上的Quillen行列式研究维滕亏格的方法。我们希望这种更几何的方法，对最近的进展，对维滕属的分析解释是更适合的应用。建议的策略利用更高的gerbes的Quillen行列式的研究，从导出的模空间，维滕属的产生。在这个框架下，我们还讨论了Calabi-Yau流形和hyperk“ahler度量在障碍物中的应用.