We study the analytic and topological invariants associated with complex normal singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with respect to a fixed topological type), under the condition that the link is a rational homology sphere. The list of analytic invariants include: the geometric genus, the cohomology of certain natural line bundles, the cohomology of their restrictions on effective cycles (in a resolution), the cohomological cycle of natural line bundles, the multivariable Hilbert and Poincare series associated with the divisorial filtration, the analytic semigroup, the maximal ideal cycle. The first part contains the definition of `generic structure' based on the work of Laufer. The second technical part rely on the properties of the Abel map developed in a previous manuscript of the authors. The results can be compared with certain parallel statements from the Brill-Noether theory (and the theory of Abel map) associated with projective smooth curves, though the tools and machineries are very different.

中文翻译：

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表面奇点的阿贝尔图 II。通用分析结构

我们研究与复杂正态奇点相关的解析和拓扑不变量。我们的目标是在链接是有理同调球体的条件下，只要解析结构是通用的（相对于固定的拓扑类型），就为几个离散的解析不变量提供拓扑公式。解析不变量的列表包括：几何属、某些自然线丛的上同调、它们对有效圈的限制的上同调（在一个分辨率中）、自然线丛的上同调圈、多变量希尔伯特和庞加莱级数与除法过滤，解析半群，最大理想循环。第一部分包含基于 Laufer 工作的“通用结构”的定义。第二个技术部分依赖于作者先前手稿中开发的 Abel 地图的属性。结果可以与 Brill-Noether 理论（和 Abel 映射理论）中与投影平滑曲线相关的某些平行陈述进行比较，尽管工具和机器非常不同。