Related papers: Hermitian Maass lift for General Level

Let $B/F$ be a quaternion algebra over a totally real number field. We give an explicit formula for heights of special points on the quaternionic Shimura variety associated with $B$ in terms of Faltings heights of CM abelian varieties.…

We give a complete theta expression of a pair of Hermitian modular forms as an inverse period mapping of lattice polarized $K3$ surfaces. Our result gives a non-trivial relation among moduli of $K3$ surfaces, theta functions and the finite…

The bounded derived category of a finite dimensional algebra of finite global dimension is equivalent the stable category of $\mathbb{Z}$-graded modules over its trivial extension \cite{Happel}. In particular, given two derived equivalent…

This article studies typical 1-Lipschitz images of $n$-rectifiable metric spaces $E$ into $\mathbb{R}^m$ for $m\geq n$. For example, if $E\subset \mathbb{R}^k$, we show that the Jacobian of such a typical 1-Lipschitz map equals 1…

We compute the subgroup of the monodromy group of a generalized Kummer variety associated to equivalences of derived categories of abelian surfaces. The result was previously announced in arXiv:1201.0031. Mongardi showed that the subgroup…

We give a generalization of the nonexistence of level structures as Nadel, Noguchi, Hwang-To, for quasi-projective manifolds uniformized by strongly Carath\'eodory hyperbolic complex manifolds. Examples include moduli space of compact…

Let $X$ be a complex smooth projective variety of dimension $d$. Under some assumption on the cohomology of $X$, we construct mutually orthogonal idempotents in $CH_d(X \times X) \otimes \Q$ whose action on algebraically trivial cycles…

Fix a quadratic order over the ring of integers. An embedding of the quadratic order into a quaternionic order naturally gives an integral binary hermitian form over the quadratic order. We show that, in certain cases, this correspondence…

We show that the hermitian K-theory space of a commutative ring R can be identified, up to A^1-homotopy, with the group completion of the groupoid of oriented finite Gorenstein R-algebras, i.e., finite locally free R-algebras with…

The aim of this paper is to carry out an explicit construction of CAP representations of GL(2) over a division quaternion algebra with discriminant two. We first construct cusp forms on such group explicitly by lifting from Maass cusp forms…

We show that the Zagier-Eisenstein series shares its non-holomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a number of consequences, including exact…

We obtain variational formulas for holomorphic objects on Riemann surfaces with respect to arbitrary local coordinates on the moduli space of complex structures. These formulas are written in terms of a canonical object on the moduli space…

We determine the size of spaces of higher order Maass forms of even weight for cofinite discrete subgroups of PSL(2,R) with cusps. If exponential growth at the cusps is allowed, the spaces of Maass forms of a given order are as large as…

In the framework of quasi-Hermitian quantum mechanics it is shown that a weakening of the isotropy of the Hilbert-space geometry can help us to enlarge the domain of the parameters at which the evolution is unitary. The idea is tested using…

We prove that the solution of a Wess-Zumino-Witten type equation from a domain $D$ in $\mathbb{C}^m$ to the space of K\"ahler potentials can be approximated uniformly by Hermitian-Yang-Mills metrics on certain vector bundles. The key is a…

We build compact moduli spaces of Grassmannian framed bundles over a Riemann surface, essentially replacing a group by its bi-invariant compactification. We do this both in the algebraic and symplectic settings, and prove a…

This paper is the third of a series on Hamiltonian stationary Lagrangian surfaces. We present here the most general theory, valid for any Hermitian symmetric target space. Using well-chosen moving frame formalism, we show that the equations…

Based on the commutativity of scalar vector fields, an algebraic scheme is developed which leads to a privileged multi-dimensionally consistent 2n+2n-dimensional integrable partial differential equation with the associated eigenfunction…

Let $S$ be a closed and oriented surface of genus $g$ at least $2$. In this (mostly expository) article, the object of study is the space $\mathcal{P}(S)$ of marked isomorphism classes of projective structures on $S$. We show that…

Motivated by classification, up to order isomorphism, of some dense subgroups of Euclidean space that are free of minimal rank, we obtain apparently new invariants for an equivalence relation (intermediate between Hermite and Smith) on…