Search results
Results From The WOW.Com Content Network
Weight 1: The only Siegel modular form is 0. Weight 2: The only Siegel modular form is 0. Weight 3: The only Siegel modular form is 0. Weight 4: For any degree, the space of forms of weight 4 is 1-dimensional, spanned by the theta function of the E 8 lattice (of appropriate degree). The only cusp form is 0. Weight 5: The only Siegel modular ...
A 2D slice of a Calabi–Yau quintic. One such quintic is birationally equivalent to the compactification of the Siegel modular variety A 1,3 (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.
Modular form theory is a special case of the more general theory of automorphic forms, which are functions defined on Lie groups that transform nicely with respect to the action of certain discrete subgroups, generalizing the example of the modular group () ().
where T is an element of the Siegel upper half plane of degree g. This is a Siegel modular form of degree d and weight dim(L)/2 for some subgroup of the Siegel modular group. If the lattice L is even and unimodular then this is a Siegel modular form for the full Siegel modular group. When the degree is 1 this is just the usual theta function of ...
In mathematics, the Siegel upper half-space of degree g (or genus g) (also called the Siegel upper half-plane) is the set of g × g symmetric matrices over the complex numbers whose imaginary part is positive definite. It was introduced by Siegel . It is the symmetric space associated to the symplectic group Sp(2g, R).
In mathematics, the Smith–Minkowski–Siegel mass formula (or Minkowski–Siegel mass formula) is a formula for the sum of the weights of the lattices (quadratic forms) in a genus, weighted by the reciprocals of the orders of their automorphism groups. The mass formula is often given for integral quadratic forms, though it can be generalized ...
In higher dimensions, moduli of algebraic varieties are more difficult to construct and study. For instance, the higher-dimensional analogue of the moduli space of elliptic curves discussed above is the moduli space of abelian varieties, such as the Siegel modular variety. This is the problem underlying Siegel modular form theory.
It is a generalization of the Siegel modular group, and has the same relation to polarized abelian varieties that the Siegel modular group has to principally polarized abelian varieties. It is the group of automorphisms of Z 2n preserving a non-degenerate skew symmetric form. The name "paramodular group" is often used to mean one of several ...