发表机构
University of Massachusetts, Amherst; HUN-REN Alfréd Rényi Institute of Mathematics; Princeton University（阿默斯特马萨诸塞大学; HUN-REN阿尔弗雷德·雷尼数学研究所; 普林斯顿大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了环面上的亏格19和亏格2曲面上的亏格4 Lefschetz纤维化族，均只有三个节点，位于BMY线上，并给出其拓扑、实商及单值分解等性质。
AI 中文摘要
我们给出了环面上的亏格19 Lefschetz纤维化和亏格2曲面上的亏格4 Lefschetz纤维化族的显式正因子分解。所有这些例子都只有三个节点，其全空间是Bogomolov-Miyaoka-Yau线上的一般型辛4流形。在推导亏格19中的单值关系的过程中，我们获得了几个有趣的恒等式，包括将一个Dehn扭转分解为三个3阶映射类的乘积。我们证明该纤维化的全空间在拓扑上s-配边于Cartwright-Steger曲面，并确定了其实商空间直至同胚的类型。亏格4族由Bauer-Catanese纤维化的变体组成，包含45个紧致复球商微分同胚类型上的65个Lefschetz纤维化同构类。我们描述了它们的拓扑以及三个原始曲面的实商空间的拓扑。我们主因子分解中的柄单值是伪Anosov的，并且我们更一般地证明，对于BMY线上的全纯亏格4 Lefschetz纤维化，这一性质对柄生成元的任何选择都成立。
英文摘要
We give explicit positive factorizations for a genus-19 Lefschetz fibration over the torus and a family of genus-4 Lefschetz fibrations over a genus-2 surface. All these examples have only three nodes, and their total spaces are symplectic 4-manifolds of general type on the Bogomolov-Miyaoka-Yau line. In the course of deriving the monodromy relation in genus 19, we obtain several interesting identities, including a factorization of a Dehn twist into a product of three order-3 mapping classes. We show that the total space of this fibration is topologically s-cobordant to the Cartwright-Steger surface, and we determine its real quotient up to homeomorphism. The genus-4 family consists of variations of the Bauer-Catanese fibrations and contains 65 isomorphism classes of Lefschetz fibrations on 45 diffeomorphism types of compact complex ball quotients. We describe their topology and that of the real quotients of the three original surfaces. The handle monodromies in our main factorizations are pseudo-Anosov, and we show more generally that for holomorphic genus-4 Lefschetz fibrations on the BMY line, this holds for every choice of handle generators.
Comments41 pages
