Picard Modular Surface
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In mathematics, a Picard modular surface, studied by , is a
complex surface Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...
constructed as a quotient of the unit ball in C2 by a
Picard modular group In mathematics, a Picard modular group, studied by , is a group of the form SU(''J'',''L''), where ''L'' is a 3-dimensional lattice over the ring of integers of an imaginary quadratic field and ''J'' is a hermitian form on ''L'' of signature  ...
. Picard modular surfaces are some of the simplest examples of
Shimura varieties In number theory, a Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient variety of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over Q. Shimura varieties are no ...
and are sometimes used as a test case for the general theory of Shimura varieties.


See also

*
Hilbert modular surface In mathematics, a Hilbert modular surface or Hilbert–Blumenthal surface is an algebraic surface obtained by taking a quotient of a product of two copies of the upper half-plane by a Hilbert modular group. More generally, a Hilbert modular varie ...
*
Siegel modular variety In mathematics, a Siegel modular variety or Siegel moduli space is an algebraic variety that parametrizes certain types of abelian varieties of a fixed dimension. More precisely, Siegel modular varieties are the moduli spaces of principally pola ...


References

* *{{Citation , last1=Picard , first1=Émile , authorlink=Émile Picard, title= Sur une extension aux fonctions de deux variables du problème de Riemann relatif aux fonctions hypergéométriques , url= http://www.numdam.org/item?id=ASENS_1881_2_10__305_0 , year=1881 , journal=Annales Scientifiques de l'École Normale Supérieure , series=Série 2 , volume=10 , pages=305–322 Complex surfaces Algebraic surfaces Automorphic forms Langlands program