论文标题
符号坐标中的HCSCK方程
The HcscK equations in symplectic coordinates
论文作者
论文摘要
Donaldson-FujikiKähler的减少了兼容的几乎复杂结构的空间，从而将Kähler指标标态曲率解释为矩图，可以将典型地提起到Hyperkähler还原。唐纳森（Donaldson）提议将相应的消失力矩条件视为希钦方程的（完全非线性）类似物，为此，基础捆绑包被偏振歧管所取代。但是，仅在复杂曲线的情况下才能很好地理解这种结构。在本文中，我们研究了唐纳森（Donaldson）的Hyperkähler减少对Abelian品种和复曲面的歧管。我们获得了一个脱钩结果，一个变异表征，与折叠情况下的$ k $稳定性的关系，并在``higgs tensor''的适当假设下证明存在和独特性。我们还与希格斯捆绑包讨论了类比的某些方面。
The Donaldson-Fujiki Kähler reduction of the space of compatible almost complex structures, leading to the interpretation of the scalar curvature of Kähler metrics as a moment map, can be lifted canonically to a hyperkähler reduction. Donaldson proposed to consider the corresponding vanishing moment map conditions as (fully nonlinear) analogues of Hitchin's equations, for which the underlying bundle is replaced by a polarised manifold. However this construction is well understood only in the case of complex curves. In this paper we study Donaldson's hyperkähler reduction on abelian varieties and toric manifolds. We obtain a decoupling result, a variational characterisation, a relation to $K$-stability in the toric case, and prove existence and uniqueness under suitable assumptions on the ``Higgs tensor''. We also discuss some aspects of the analogy with Higgs bundles.
