The Classification of Hilbert Modular Surfaces
The Classification of Hilbert Modular Surfaces
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希尔伯特模曲面的分类
DOI：
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发表时间：
1988
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通讯作者：
G. Geer
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作者：
G. Geer
在接下来的两章中，重点是希尔伯特模曲面的几何。代数曲面是根据其复属的增长来分类的，粗略地说，这是一种度量典型因子类的丰富度的方法。在Hilbert模曲面上，我们在某种意义上有两个“典型因子类”，通常的典型类c1（Ω 2）和类c1（Ω 2（logD）），D是分解尖点的因子。第二个是更自然的Hilbert模曲面，但通过使用第一个代数曲面的标准理论成为可用。由于如果Γ π 2的体积较大，则c1（Ω 2（logD））和c1（Ω 2）的差值D相对较小，因此一般认为这两类的行为相似。
In the next two chapters the emphasis is on the geometry of Hilbert modular surfaces. Algebraic surfaces are classified by the growth of their plurigenera, which roughly speaking is a way of measuring the ampleness of the canonical divisor class. On Hilbert modular surfaces we have in some sense two “canonical divisor classes”, the usual canonical class c 1 (Ω 2 ) and the class c 1(Ω 2(logD)) with D the divisor resolving the cusps. The second one is more natural for Hilbert modular surfaces, but by using the first one the standard theory of algebraic surfaces becomes available. Since the difference D of c 1 (Ω 2 (logD)) and c 1 (Ω 2 ) is relatively small if the volume of Γℌ 2is big one expects in general that the two classes behave similarly.