论文标题
与稳定的希格斯束系列有关的曲率公式
Curvature formulas related to a family of stable Higgs bundles
论文作者
论文摘要
在本文中，我们研究了有效参数化的稳定希格斯束的有效参数化的全态家族的几何形状，这是固定的紧凑型kähler歧管上的几何形状。我们研究的起点是Schumacher-Toma/Biswas-Schumacher的曲率公式，用于Weil-petersson-type指标。 2，我们在基本歧管的几何特性上提供了其公式的一些应用。昆虫。 3，我们计算较高的直接图像束上的曲率，该图像束恢复了Biswas-Schumacher的曲率公式。昆虫。 4，我们为基础歧管构建平滑且强烈的伪符号复合鳍度量指标，明确计算相应的圆锥形截面曲率。
In this paper, we investigate the geometry of the base complex manifold of an effectively parametrized holomorphic family of stable Higgs bundles over a fixed compact Kähler manifold. The starting point of our study is Schumacher-Toma/Biswas-Schumacher's curvature formulas for Weil-Petersson-type metrics, in Sect. 2, we give some applications of their formulas on the geometric properties of the base manifold. In Sect. 3, we calculate the curvature on the higher direct image bundle, which recovers Biswas-Schumacher's curvature formula. In Sect. 4, we construct a smooth and strongly pseudo-convex complex Finsler metric for the base manifold, the corresponding holomorphic sectional curvature is calculated explicitly.
