Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Hilbert modular variety
open-in-new
<p>In mathematics, a Hilbert modular surface or Hilbert–Blumenthal surface is an <a href="/facts/Algebraic_surface/2zHU0o9J">algebraic surface</a> obtained by taking a quotient of a product of two copies of the <a href="/facts/Upper_half-plane/7fPqrowr">upper half-plane</a> by a <a href="/facts/Hilbert_modular_group/BjIRAzCX">Hilbert modular group</a>. More generally, a Hilbert modular variety is an <a href="/facts/Algebraic_variety/Vk7f97vn">algebraic variety</a> obtained by taking a quotient of a product of multiple copies of the upper half-plane by a Hilbert modular group. </p><p>Hilbert modular surfaces were first described by Otto Blumenthal (1903, 1904) using some unpublished notes written by <a href="/facts/David_Hilbert/1vhlHn4b">David Hilbert</a> about 10 years before. </p>