algebraic variety that is a moduli space for principally polarized abelian varieties
a 2d slice of a calabi–yau quintic. one such quintic is birationally equivalent to the compactification of the siegel modular variety a1,3(2).
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 polarized abelian varieties of a fixed dimension. they are named after carl ludwig siegel, a 20th-century german mathematician who specialized in number theory. he introduced siegel modular varieties in a 1943 paper.
siegel modular varieties are the most basic examples of shimura varieties. siegel modular varieties generalize moduli spaces of algebraic curves to higher dimensions and play a central role in the theory of siegel modular forms, which generalize classical modular forms to higher dimensions. they also have applications to black hole entropy and conformal field theory.