发表机构
School of Science, Nanjing University of Posts and Telecommunications（南京邮电大学理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文构造了两族以二维复环面为纤维的紧致复三维流形，计算了其拓扑不变量，并证明每个光滑六维流形上存在不可数多个非双全纯的复结构。
AI 中文摘要
我们构造了两个以二维复环面为纤维、底空间为$\mathbb P^1$的紧致复三维流形族。对于每个正整数$r$和固定半平面中的每个参数$c$，族$Y_{r,c}$和$Z_{r,c}$分别具有两个重数为$(4,6)$和$(3,6)$的多重纤维，以及一个约化法交叉纤维，其正规化由$r$个六次del Pezzo曲面组成。它们的基本群分别为$\mathbb Z/2$和$\mathbb Z/3$，且两者的欧拉示性数均为$2r$。我们计算了它们的积分同调；指数为一的成员是有理同调六维球面。每个成员的代数维数为一，位于Fujiki类$\mathcal C$之外，且其自同构群连通，为$\mathbb C^*$。对于固定类型和指数，两个成员双全纯等价当且仅当它们的参数相差$(6/r)\mathbb Z$中的元素。因此，每个底层的光滑六维流形支持不可数多个两两非双全纯的复结构。算术输入分类了有限单值对及其在作用于秩四格上的抛物Jacobi群中的积分提升。一个二次型控制积分提升，并在秩二平方零轨迹上计算单值饱和指数。我们证明了相关的不变张量在有限指数限制下保持不变，这将该构造推广到任意紧致底曲线。我们还在基变换后构造了平移扭曲，建立了任意维度的局部周期环面商定理，并确定了原始三维流形的加性Bockstein谱序列。
英文摘要
We construct two families of compact complex threefolds fibred over $\mathbb P^1$ by two-dimensional complex tori. For each positive integer $r$ and each parameter $c$ in a fixed half-plane, the families $Y_{r,c}$ and $Z_{r,c}$ have two multiple fibres of multiplicities $(4,6)$ and $(3,6)$, respectively, and one reduced normal-crossings fibre whose normalization consists of $r$ del Pezzo surfaces of degree six. Their fundamental groups are $\mathbb Z/2$ and $\mathbb Z/3$, respectively, and both have Euler characteristic $2r$. We compute their integral homology; the index-one members are rational homology six-spheres. Every member has algebraic dimension one, lies outside Fujiki's class $\mathcal C$, and has connected automorphism group $\mathbb C^*$. For fixed type and index, two members are biholomorphic exactly when their parameters differ by an element of $(6/r)\mathbb Z$. Each underlying smooth six-manifold therefore supports uncountably many pairwise non-biholomorphic complex structures. The arithmetic input classifies finite monodromy pairs and their integral lifts to a parabolic Jacobi group acting on a rank-four lattice. A quadratic form controls integral lifting and, on the rank-two square-zero locus, computes the monodromy saturation index. We prove that the relevant invariant tensors persist under finite-index restriction, which extends the construction to arbitrary compact base curves. We also construct translation twists after base change, establish a local periodic toroidal quotient theorem in arbitrary dimension, and determine the additive Bockstein spectral sequences of the original threefolds.
Comments74 pages
