Hilbert modular variety

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 variety is an algebraic variety obtained by taking a quotient of a product of multiple copies of the upper half-plane by a Hilbert modular group.

Hilbert modular surfaces were first described by Otto Blumenthal (1903, 1904) using some unpublished notes written by David Hilbert about 10 years before.