Spectral Data of Finite Type Almost Complex Curves in 6-Sphere
主 题: Spectral Data of Finite Type Almost Complex Curves in 6-Sphere
报告人: Dr. Wang Erxiao (新加坡国立大学)
时 间: 2009-01-02 下午 2:00 - 3:00
地 点: 理科一号楼 1114(数学所活动)
The talk will focus on the interesting background and a beautiful dictionary between a class of differential equations and Riemann surface (or algebraic curve) theory, thus for general audiences including graduate students. We will establish a bijective correspondence between finite type almost complex curves in S^6 and their spectral data, which consists of a hexagonal algebraic curve and a planar flow of line bundles in its Jacobian. We characterize the spectral data by identifying various symmetries on them. We prove generic smoothness of these spectral curves, compute their genus, and compute the dimension of the moduli of such curves. Then we identify a Prym-Tjurin subtorus of the Jacobian, in which the direction of the flow must lie, and compute its dimension. Finally we characterize finite type special Lagrangian cones in C^3 as a subclass of such associative cones in terms of the spectral data. These computations are mainly motivated by Hitchin\'s recent work on Langland duality.
