Related papers: Siegel operators for holomorphic differential form…
We introduce a method in differential geometry to study the derivative operators of Siegel modular forms. By determining the coefficients of the invariant Levi-Civita connection on a Siegel upper half plane, and further by calculating the…
In this paper we study mixed Hodge structures on the cohomology of locally symmetric varieties and give an application to modular forms. After proving vanishing of some Hodge numbers, we focus on the weight filtration on the last Hodge…
We describe the effect of the differential operators defined by Boecherer-Nagaoka, Flander-Ghitza and Yamauchi on the Galois representations (conjecturally) attached to Siegel modular eigenforms.
In this paper, we decompose the space of nearly holomorphic Hilbert-Siegel automorphic forms as representations of the adele group under certain assumptions. We also give an application for classical holomorphic Hilbert-Siegel modular…
If $a$ is a densely defined sectorial form in a Hilbert space which is possibly not closable, then we associate in a natural way a holomorphic semigroup generator with $a$. This allows us to remove in several theorems of semigroup theory…
We define Hilbert-Siegel modular forms and Hecke "operators" acting on them. As with Hilbert modular forms, these linear transformations are not linear operators until we consider a direct product of spaces of modular forms (with varying…
This is a survey article about Siegel modular varieties over the complex numbers. It is written mostly from the point of view of moduli of abelian varieties, especially surfaces. We cover compactification of Siegel modular varieties;…
We define Hecke operators on vector valued modular forms transforming with the Weil representation associated to a discriminant form. We describe the properties of the corresponding algebra of Hecke operators and study the action on modular…
We study the hyperbolicity of compactifications of quotients of bounded symmetric domains by arithmetic groups. We prove that, up to an \'etale cover, they are Kobayashi hyperbolic modulo the boundary. Applying our techniques to Siegel…
In this paper, we prove some divisibility results for the Fourier coefficients of reduced modular forms of sign vectors. More precisely, we generalize a divisibility result of Siegel on constant terms when the weight is non-positive, which…
We use vanishing results for sheaf cohomology on Siegel modular varieties to study two lifting problems: (a) When can Siegel modular forms (mod p) be lifted to characteristic zero? This uses and extends previous results for cusp forms by…
We classify the $(\mathfrak{g},K)$-modules generated by nearly holomorphic Hilbert-Siegel modular forms by the global method. As an application, we study the image of projection operators on the space of nearly holomorphic Hilbert-Siegel…
In the spirit of the geometric approach to two-dimensional conformal field theory, we explicitly associate to every holomorphic vertex operator algebra a section of a power of Hodge line bundle on the moduli space of curves of arbitrary…
In this paper, we discuss the theory of the Siegel modular variety in the aspects of arithmetic and geometry. This article covers the theory of Siegel modular forms, the Hecke theory, a lifting of elliptic cusp forms, geometric properties…
We consider several differential operators on compact almost-complex, almost-Hermitian and almost-K\"ahler manifolds. We discuss Hodge Theory for these operators and a possible cohomological interpretation. We compare the associated spaces…
We give a complete classification of conformally covariant differential operators between the spaces of differential $i$-forms on the sphere $S^n$ and $j$-forms on the totally geodesic hypersphere $S^{n-1}$ by analyzing the restriction of…
We study the cone of moving divisors on the moduli space ${\mathcal A}_g$ of principally polarized abelian varieties. Partly motivated by the generalized Rankin-Cohen bracket, we construct a non-linear holomorphic differential operator that…
Every four-dimensional ${\cal N}=2$ superconformal field theory comes equipped with an intricate algebraic invariant, the associated vertex operator algebra. The relationships between this invariant and more conventional protected…
Invited talk at the International Symposium on Generalized Symmetries in Physics at the Arnold-Sommerfeld-Institute, Clausthal, Germany, July 26 -- July 29, 1993. This talk reviews results on the structure of algebras consisting of…
We calculate the action of some Hecke operators on spaces of modular forms spanned by the Siegel theta-series of certain genera of strongly modular lattices closely related to the Leech lattice. Their eigenforms provide explicit examples of…