The transition constant for arithmetic hyperbolic reflection groups

Details The transition constant for arithmetic hyperbolic reflection groups The transition constant for arithmetic hyperbolic reflection groups

2009-10-27

arxiv.org/abs/0910.5217v4

Izvestiya RAN: Ser.Mat. 75:5, 2011, 103-138 (Russian); English translation in Izvestiya:Mathematics 75:5, 2011, 971-1005

Mathematics

Algebraic Geometry

Var4: results improved, 37 pages

Scientific paper

The transition constant was introduced in our 1981 paper and denoted as N(14). It is equal to the maximal degree of the ground fields of V-arithmetic connected edge graphs with 4 vertices and of the minimality 14. This constant is fundamental since if the degree of the ground field of an arithmetic hyperbolic reflection group is greater than N(14), then the field comes from very special plane reflection groups. In our recent paper (see also arXiv:0708.3991), we claimed its upper bound 56. Using similar but more difficult considerations, here we improve this bound. These results could be important for further classification.

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