%0 Generic %1 francsics2005explicit %A Francsics, Gábor %A Lax, Peter D. %D 2005 %K domain explicit fundamental modular picard %T An explicit fundamental domain for the Picard modular group in two complex dimensions %U http://arxiv.org/abs/math/0509708 %X Our main goal in this paper is to construct the first explicit fundamental domain of the Picard modular group acting on the complex hyperbolic space $\bf CH^2$. The complex hyperbolic space is a Hermitian symmetric space, its bounded realization is the unit ball in $C^2$ equipped with the Bergman metric. The Picard modular group is a discontinuous holomorphic automorphism subgroup of $SU(2,1)$ with Gaussian integer entries. This fundamental domain has finite volume, one cusp, explicitly given boundary surfaces and an interesting symmetry.

@misc{francsics2005explicit, abstract = {Our main goal in this paper is to construct the first explicit fundamental domain of the Picard modular group acting on the complex hyperbolic space ${\bf CH}^{2}$. The complex hyperbolic space is a Hermitian symmetric space, its bounded realization is the unit ball in ${\bf C}^2$ equipped with the Bergman metric. The Picard modular group is a discontinuous holomorphic automorphism subgroup of $SU(2,1)$ with Gaussian integer entries. This fundamental domain has finite volume, one cusp, explicitly given boundary surfaces and an interesting symmetry.}, added-at = {2013-12-23T06:45:50.000+0100}, author = {Francsics, Gábor and Lax, Peter D.}, biburl = {https://www.bibsonomy.org/bibtex/237ac3aa7f74d45dfa0ec030f6718b0f4/aeu_research}, description = {An explicit fundamental domain for the Picard modular group in two complex dimensions}, interhash = {728413bd13c2c769fa0e769db6599e09}, intrahash = {37ac3aa7f74d45dfa0ec030f6718b0f4}, keywords = {domain explicit fundamental modular picard}, note = {cite arxiv:math/0509708Comment: 25 pages}, timestamp = {2013-12-23T06:45:50.000+0100}, title = {An explicit fundamental domain for the Picard modular group in two complex dimensions}, url = {http://arxiv.org/abs/math/0509708}, year = 2005 }