论文标题
标态曲率和复杂结构的变形
Scalar curvature and deformations of complex structures
论文作者
论文摘要
我们在紧凑的复杂歧管上研究了方程系统，该方程式将kaehler度量的标态曲率与复合结构的一阶变形的光谱函数结合在一起。该系统来自无限尺寸的kaehler降低，这是特定选择光谱函数的超杀手降低。该系统可以使用与Kaehler度量兼容的一阶变形空间上的平坦连接正式化。我们描述了方程式的变异表征，该系统的futaki不变性以及K稳定性的概括，以表征系统的解决方案。我们在复曲面的背景下验证了这种猜想的特定情况。
We study a system of equations on a compact complex manifold, that couples the scalar curvature of a Kaehler metric with a spectral function of a first-order deformation of the complex structure. The system comes from an infinite-dimensional Kaehler reduction, which is a hyperkaehler reduction for a particular choice of the spectral function. The system can be formally complexified using a flat connection on the space of first-order deformations that are compatible with a Kaehler metric. We describe a variational characterization of the equations, a Futaki invariant for the system, and a generalization of K-stability that is conjectured to characterize the existence of solutions to the system. We verify a particular case of this conjecture in the context of toric manifolds.
