Related papers: Modules of square integrable holomorphic germs

In this note we identify two complex structures (one is given by algebraic geometry, the other by gauge theory) on the set of isomorphism classes of holomorphic bundles with section on a given compact complex manifold. In the case of line…

We deduce from the work of Chen, that the restriction morphism from closed free iterated integrals to closed iterated integrals on loops is onto. We use this to show that the module of higher order invariants of smooth functions is…

This is an expository article. In the first part we recall the definition and a few results concerning singular Hermitian metrics on torsion-free coherent sheaves. They offer the perfect platform for the study of properties of direct images…

A general theory of vector-valued modular functions, holomorphic in the upper half-plane, is presented for finite dimensional representations of the modular group. This also provides a description of vector-valued modular forms of arbitrary…

Let $\Omega \subset \mathbb{C}^m$ be an open, connected and bounded set and $\mathcal{A}(\Omega)$ be a function algebra of holomorphic functions on $\Omega$. In this article we study quotient Hilbert modules obtained from submodules,…

For the purpose of proving the strong openness conjecture of multiplier ideal sheaves, Jonsson-Musta\c{t}\u{a} posed an enhanced conjecture and proved the two-dimensional case, which says that: the Lebesgue measure of the set…

In modular invariant models of flavor, observables must be modular invariant. The observables discussed so far in the literature are functions of the modulus $\tau$ and its conjugate, $\bar\tau$. We point out that certain combinations of…

The goal of this article is to establish tauberian theorems for the $k$--summability processes defined by germs of analytic functions in several complex variables. The proofs are based on the tauberian theorems for $k$--summability in one…

Many Hilbert modules over the polynomial ring in m variables are essentially reductive, that is, have commutators which are compact. Arveson has raised the question of whether the closure of homogeneous ideals inherit this property and…

In this work we show two results about approximating, with respect to the compact-open topology, mapping classes on surfaces of infinite-type by quasi-conformal maps, in particular we are interested in density results. The first result is…

In their 2015 paper, Mertens and Rolen prove that for a certain level 6 "almost holomorphic" modular function $P$, the degree of $P(\tau)$ over $\mathbb{Q}$ for quadratic $\tau$ is as large as expected, settling a conjecture of Bruinier and…

In previous work, we have introduced delta-forms on the Berkovich analytification of an algebraic variety in order to study smooth or formal metrics via their associated Chern delta-forms. In this paper, we investigate positivity properties…

Let $E\to M$ be a holomorphic vector bundle over a compact Kaehler manifold $(M, \omega)$. We prove that if $E$ admits a $\omega$-balanced metric (in X. Wang's terminology) then it is unique. This result together with a result of L.…

By applying holomorphic motions, we prove that a parabolic germ is quasiconformally rigid, that is, any two topologically conjugate parabolic germs are quasiconformally conjugate and the conjugacy can be chosen to be more and more near…

We formalize the ``metric bundle'' viewpoint by defining, for any smooth $n$--manifold $M$, the open fiberwise cones $\mathcal{G}^{p,q}\subset S^2\Tstar M$ of nondegenerate symmetric bilinear forms with fixed signature $(p,q)$, and we…

Let $E$ be a holomorphic vector bundle endowed with a singular Hermitian metric $H$. In this paper, we develop the harmonic theory on $(E,H)$. Then we extend several canonical results of J. Koll\'{a}r and K. Takegoshi to this situation. In…

Let $X$ be a complex analytic curve. In this paper we prove that the subanalytic sheaf of tempered holomorphic solutions of $\mathcal D_X$-modules induces a fully faithful functor on a subcategory of germs of formal holonomic $\mathcal…

In this article, we consider Bergman kernels with respect to modules at boundary points, and obtain a log-subharmonicity property of the Bergman kernels, which deduces a concavity property related to the Bergman kernels. As applications, we…

We introduce a notion of admissible Hermitian metrics on parabolic bundles and define positivity properties for the same. We develop Chern-Weil theory for parabolic bundles and prove that our metric notions coincide with the already…

We construct bases of quasi-symmetric functions whose product rule is given by the shuffle of binary words, as for multiple zeta values in their integral representations, and then extend the construction to the algebra of free…