Characteristic Cycles and Representation Theory

该项目结合了经典的代数几何与代数分析和拓扑学的方法。它的主要目标是通过反常层和D-模的理论来研究阿贝尔簇的子簇。在这方面，余切丛上的特征圈扮演着核心角色，它捕捉了关于奇点和分歧的微妙信息。他们将高斯映射与Tannakian形式主义所产生的线性代数群的表示联系起来。这两种观点的结合很可能会在代数几何中找到应用，并提高我们对Tannakian群的理解。

The project combines classical algebraic geometry with methods from algebraic analysis and topology. Its main goal is to study subvarieties of abelian varieties via the theory of perverse sheaves and D-modules.In this context a central role is played by characteristic cycles on the cotangent bundle, which capture subtle information on singularities and ramification. They relate Gauss maps to the representations of linear algebraic groups arising from the Tannakian formalism. The combination of both viewpoints is likely to find applications in algebraic geometry and improve our understanding of the arising Tannakian groups.