On discontinuous action of monodromy groups on the complex $n$-ball
On discontinuous action of monodromy groups on the complex $n$-ball
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论单群群对复杂 $n$-球的不连续作用
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发表时间：
1988
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通讯作者：
G. Mostow
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作者：
G. Mostow
在[DM，3.10，3.15]中，为每个(n+3)元组(1U，..N+3)具有Ei2的非整实数，i积分作用在n+1维复向量空间Vj上的子群i，它保持签名的Hermite形式((Zi(P))1，(Ei(1ui))1)[Dm，2.21]，其中对于任何实数r，(R)表示其分数部分，即0}。我们将主要考虑厄米特形式的签名是(1正，n负)的情况，在这种情况下，V+在与V相关联的射影空间Pn中的像是复n球Bn(也称为n盘)。我们几乎只讨论F在Bn和Pn上的作用。我们称一个(n+3)元组为圆盘(n+3)元组，当i=1.n+3且Eiz i=2时，u满足0<；pi<；1。在[DM，定理10.19]中证明了：设u是满足条件int的圆盘(n+3)元组：对于所有i：aj使得，ui+uj<；1，
In [DM, 3.10, 3.15] there is defined for each (n + 3)-tuple (1u, .. n+3) of nonintegral real numbers with Ei2,i integral a subgroup I,, acting on a complex (n + 1)-dimensional vector space VJ, which preserves a hermitian form of signature ((Zi(p)) 1, (Ei(1 ui)) 1) [DM, 2.21], where for any real number r, (r) denotes its fractional part, i.e., 0 0} . We will be concerned principally with the case that the signature of the hermitian form is (1 positive, n negative) in which case the image of V+ in the projective space pn associated to V is the complex n-ball Bn (also called the n-disc). We deal almost exclusively with the action of F, on Bn and pn . We call an (n + 3)-tuple ,u satisfying 0 < pi < 1 for i = 1. n + 3 and EiZ i = 2 a disc (n + 3)-tuple. In [DM, Theorem 10. 19] it is proved: Let ,u be a disc (n + 3)-tuple satisfying condition INT: for all i :A j such that ,ui + uj < 1,