## Siegel modular variety |

In mathematics, a **Siegel modular variety** or **Siegel moduli space** is an ^{[2]} a 20th century German mathematician who specialized in ^{[2]} Siegel modular varieties in a 1943 paper.^{[3]}

Siegel modular varieties are the most basic examples of ^{[4]} Siegel modular varieties generalize ^{[1]} They also have applications to ^{[5]}

- construction
- properties
- applications
- see also
- references

The Siegel modular variety *A*_{g}, which parametrize principally polarized abelian varieties of dimension *g*, can be constructed as the *g* by the action of a ^{[1]}

The Siegel modular variety *A*_{g}(*n*), which parametrize principally polarized abelian varieties of dimension *g* with a *n*-structure*n* of a symplectic group.^{[1]}

A Siegel modular variety may also be constructed as a Shimura variety defined by the Shimura datum associated to a ^{[4]}