Line bundles on toroidal groups.
Line bundles on toroidal groups.
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环形组上的线束。
DOI：
10.1515/crll.1982.335.197
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发表时间：
1982
期刊：
影响因子：
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通讯作者：
C. Vogt
中科院分区：
文献类型：
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作者：
C. Vogt
这是一个著名的经典结果，在复环面上，即C与最大秩为2«的格的商，每个除数都是函数的除数。在本文中，我们讨论了C在格上的商不一定是极大秩r的问题。我们限制了环面群的情况，即C在格上的商X=C/ a，使得X上的所有全纯函数都是常数。根据Remmert和Morimoto（[4]和[6]）的一个定理，格上C的每一个商都同构于C的拷贝、C*:= C\{0}的拷贝和环面群的直积。复环面就是紧化环面群。
It is a well-known classical result that on a complex torus, i.e. a quotient of C by a lattice of maximal rank 2«, every divisor is the divisor of a theta function. In this paper we would like to pursue this question for quotients of C by a lattice Ar of not necessarily maximal rank r. We restrict ourselves to the case of toroidal groups, i.e. quotients X=C/A of C by a lattice such that all holomorphic functions on X are constant. By a theorem of Remmert and Morimoto ([4] and [6]) every quotient of C by a lattice is isomorphic to the direct product of copies of C, copies of C*:= C\{0}, and a toroidal group. The complex tori are exactly the compact toroidal groups.