FANO SHIMURA VARIETIES WITH MOSTLY BRANCHED CUSPS
FANO SHIMURA VARIETIES WITH MOSTLY BRANCHED CUSPS
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发表时间：
2021
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通讯作者：
Yota Maeda;Y. Odaka
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作者：
Yota Maeda;Y. Odaka
利用特殊的模形式证明了某些Shimura簇的Satake-Bachelor-Borel紧化是Fano簇或具有充分的标准因子，并给出了各种具体的例子.它们的无分支开子集总是拟仿射的，例如在Fano酉Shimura簇的情况下，除了一个尖点之外，所有的尖点都必然被分支因子的闭包所覆盖。我们的例子包括模的（日志）Enriques表面，那些对应于II 2，26，和那些相关的各种厄米晶格。同时，我们还证明了对于某些虚二次域和任何幺模埃尔米特格，相应的酉Shimura簇在余维1上是无分支的。
We show the Satake-Baily-Borel compactification of certain Shimura varieties are Fano varieties or with ample canonical divisor by means of special modular forms and give various concrete examples. Their unbranched open subsets are always quasi-affine and in Fano unitary Shimura varieties case for instance, all but one cusps are necessarily covered by the closure of branch divisors. Our examples include the moduli of (log) Enriques surfaces, those corresponding to II2,26, and those associated to various Hermitian lattices. On the way, we also show that for some imaginary quadratic fields and any unimodular Hermitian lattices, the associated unitary Shimura varieties are unbranched in codimension 1.