Siegel modular variety

  • 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).[1]

    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,[2] a 20th-century german mathematician who specialized in number theory. he introduced[2] siegel modular varieties in a 1943 paper.[3]

    siegel modular varieties are the most basic examples of shimura varieties.[4] 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.[1] they also have applications to black hole entropy and conformal field theory.[5]

  • construction
  • properties
  • applications
  • see also
  • references

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).[1]

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,[2] a 20th-century German mathematician who specialized in number theory. He introduced[2] Siegel modular varieties in a 1943 paper.[3]

Siegel modular varieties are the most basic examples of Shimura varieties.[4] 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.[1] They also have applications to black hole entropy and conformal field theory.[5]

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