The Burkhardt group and modular forms

被引：13
|
作者：
Freitag, E
Manni, RS
机构：
[1] Math Inst, D-69120 Heidelberg, Germany
[2] Dipartimento Matemat, I-00185 Rome, Italy
来源：
TRANSFORMATION GROUPS | 2004年 / 9卷 / 01期
关键词：
D O I：
10.1007/s00031-004-7002-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we investigate the ring of Siegel modular forms of genus two and level 3. We determine the structure of this ring. It is generated by 10 modular forms (5 of weight 1 and 5 of weight 3) and there are 20 relations (5 in weight 5 and 15 in weight 6). The proof consists of two steps. In a first step we prove that the Satake compactification of the modular variety of. genus 2 and level 3 is the normalization of the dual of the Burkhardt quartic. The second part consists in the normalization of the Burkhardt dual. Our basic tool is the representation theory of the Burkhardt group G = G(25920), which acts on our varieties.
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收藏
页码：25 / 45
页数：21
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