The dimension of the image of the Abel map associated with normal surface singularities
The dimension of the image of the Abel map associated with normal surface singularities
复制标题
与法线表面奇点相关的阿贝尔图图像的维数
DOI：
10.1007/s00029-022-00777-z
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
A. N'emethi
中科院分区：
文献类型：
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作者：
János Nagy;A. N'emethi
设 (X,o) 为具有有理同调球面链接的复法线表面奇点，并设 为其良好分辨率之一。考虑异常曲线上支持的有效环Z和Z上线束的同构类。的可能值集可以根据阿贝尔图图像的维度来理解，即 的子空间。在本文中，我们提出了两种提供这些维度的算法。通常，阿贝尔图的图像的维数和维数不是拓扑的。然而，只要解析结构是通用的，我们就根据分辨率图为它们提供组合公式。
Let (X,o) be a complex normal surface singularity with rational homology sphere link and letbe one of its good resolutions. Consider an effective cycleZsupported on the exceptional curve and the isomorphism classesof line bundles onZ. The set of possible valuesforcan be understood in terms of the dimensions of the images of the Abel maps, as subspaces of. In this note we present two algorithms, which provide these dimensions. Usually, the dimension ofand of the dimension of the image of the Abel maps are not topological. However, we provide combinatorial formulae for them in terms of the resolution graph whenever the analytic structure onis generic.