论文标题
对数霍奇模量空间的几何形状（带有Siqing Zhang的附录关节）
Geometry of the logarithmic Hodge moduli space (with an Appendix joint with Siqing Zhang)
论文作者
论文摘要
我们显示了共晶等级和学位的对数T连接的霍奇模量空间的仿射线上的平滑度，该连接在平滑的射击曲线上，在任意noetherian碱基上具有几何积分纤维。当基座是一个字段时，我们还证明了霍奇模量空间是几何积分的。一路上，我们证明了对数希格斯束和对数连接的相应模量空间相同的结果。 我们利用平滑度来得出这些模量空间的依托同构的专业化同构。这包括当基础混合特征时的特殊情况。在基础是一个阳性特征的闭合场的特殊情况下，我们表明这些同构是与相应的Hitchin型形态相关的不良过滤的过滤同构。
We show the smoothness over the affine line of the Hodge moduli space of logarithmic t-connections of coprime rank and degree on a smooth projective curve with geometrically integral fibers over an arbitrary Noetherian base. When the base is a field, we also prove that the Hodge moduli space is geometrically integral. Along the way, we prove the same results for the corresponding moduli spaces of logarithmic Higgs bundles and of logarithmic connections. We use smoothness to derive specialization isomorphisms on the etale cohomology rings of these moduli spaces; this includes the special case when the base is of mixed characteristic. In the special case where the base is a separably closed field of positive characteristic, we show that these isomorphisms are filtered isomorphisms for the perverse filtrations associated with the corresponding Hitchin-type morphisms.
