The Hirzebruch-Mumford volume for the orthogonal group and applications
نویسنده
چکیده
In this paper we derive an explicit formula for the HirzebruchMumford volume of an even lattice L of signature (2, n). If Γ ⊂ O(L) is an arithmetic subgroup, then an application of Hirzebruch-Mumford proportionality allows us to determine the leading term of the growth of the dimension of the spaces Sk(Γ) of cusp forms of weight k, as k goes to infinity. We compute this in a number of examples, which are important for geometric applications.
منابع مشابه
F eb 2 00 6 The Hirzebruch - Mumford volume for the orthogonal group and applications
In this paper we derive an explicit formula for the HirzebruchMumford volume of an indefinite lattice L of rank ≥ 3. If Γ ⊂ O(L) is an arithmetic subgroup and L has signature (2, n), then an application of Hirzebruch-Mumford proportionality allows us to determine the leading term of the growth of the dimension of the spaces Sk(Γ) of cusp forms of weight k, as k goes to infinity. We compute this...
متن کاملK-theoretic and Categorical Properties of Toric Deligne–mumford Stacks
We prove the following results for toric Deligne–Mumford stacks, under minimal compactness hypotheses: the Localization Theorem in equivariant K-theory; the equivariant Hirzebruch–Riemann–Roch theorem; the Fourier–Mukai transformation associated to a crepant toric wall-crossing gives an equivariant derived equivalence.
متن کاملRelative volume comparison theorems in Finsler geometry and their applications
We establish some relative volume comparison theorems for extremal volume forms of Finsler manifolds under suitable curvature bounds. As their applications, we obtain some results on curvature and topology of Finsler manifolds. Our results remove the usual assumption on S-curvature that is needed in the literature.
متن کاملORTHOGONAL ZERO INTERPOLANTS AND APPLICATIONS
Orthogonal zero interpolants (OZI) are polynomials which interpolate the “zero-function” at a finite number of pre-assigned nodes and satisfy orthogonality condition. OZI’s can be constructed by the 3-term recurrence relation. These interpolants are found useful in the solution of constrained approximation problems and in the structure of Gauss-type quadrature rules. We present some theoretical...
متن کاملFixed point results for Ʇ_Hθ- contractive mappings in orthogonal metric spaces
The main purpose of this research is to extend some fixed point results in orthogonal metric spaces. For this purpose, first, we investigate new mappings in this spaces. We introduce the new notions of functions. Then by using it, we define contractive mappings and then we establish and prove some fixed point theorems for such mappings in orthogonal metric spaces. Then by utilizing examples of ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1998