Algebraic surfaces of general type with
Algebraic surfaces of general type with
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一般类型的代数曲面
DOI：
10.1080/00927872.2021.1994582
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发表时间：
2021
影响因子：
0.7
通讯作者：
Songbo Ling
中科院分区：
文献类型：
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作者：
Songbo Ling
本文研究了一般型极小代数曲面，由于Horikawa，Zucconi和Bauer已经研究过这种情况，我们在这里总是假设。我们证明了，对于这样的曲面，典型的映射是一般有限的1或2度。若正则映射的次数为2，则正则像是直纹曲面，而且对任意固定点都存在这样的正则曲面。如果正则映射的次数为1，则曲面是正则的（即q = 0），其正则线性系统是无基点的或有一个简单基点。在标准映射是双有理的，标准线性系统是基点自由的情况下，我们研究了它的标准像的性质，证明了对任何不动点都存在这样一个曲面。
Abstract In this paper, we study minimal algebraic surfaces of general type with Since the case has been studied by Horikawa, Zucconi, and Bauer, we always assume here. We prove that for such a surface, the canonical map is generically finite of degree 1 or 2. If the degree of the canonical map is 2, then the canonical image is a ruled surface, moreover, for any fixed there exists such a regular surface. If the degree of the canonical map is 1, then the surface is regular (i.e. q = 0) and its canonical linear system is base point free or has one simple base point. In the case where the canonical map is birational and the canonical linear system is base point free, we study the property of its canonical image and prove that for any fixed there exists such a surface.