论文标题
刚性$ g_2 $ -connections的不规则hodge数字
Irregular Hodge numbers for rigid $G_2$-connections
论文作者
论文摘要
由以有限的覆盖物沿着有限的覆盖物和傅立叶变换，在刺穿的投影线上固定的本地系统，通过命名作者构建的某些刚性不规则的$ G_2 $ - 连接是通过回调和傅立叶变换相关的。 Katz首先观察到这种特性用于超几何连接，并由Sabbah和Yu使用用于计算不规则的Hodge过滤用于超几何连接。该策略也可以应用于上述$ G_2 $ - 连接，我们为其不规则的Hodge过滤计算跳跃指数和尺寸。
Certain rigid irregular $G_2$-connections constructed by the first-named author are related via pullbacks along a finite covering and Fourier transform to rigid local systems on a punctured projective line. This kind of property was first observed by Katz for hypergeometric connections and used by Sabbah and Yu to compute irregular Hodge filtrations for hypergeometric connections. This strategy can also be applied to the aforementioned $G_2$-connections and we compute jumping indices and dimensions for their irregular Hodge filtrations.
