Related papers: The $\theta$-density in Arakelov geometry

We systematically study the moduli theory of symplectic varieties (in the sense of Beauville) which admit a resolution by an irreducible symplectic manifold. In particular, we prove an analog of Verbitsky's global Torelli theorem for the…

We prove an arithmetic Hilbert-Samuel type theorem for semi-positive singular hermitian line bundles of finite height. In particular, the theorem applies to the log-singular metrics of Burgos-Kramer-K\"uhn. Our theorem is thus suitable for…

In this paper we study the problem of density in (1,3] for the Chern ratio of surfaces with ample cotangent bundle. In particular we prove density in (1,2) by constructing a family of complete intersection surfaces in a product of varieties…

In \cite{Broer1993}, it was shown that certain line bundles on $\widetilde{\mathcal{N}}=T^*G/B$ have vanishing higher cohomology. We prove a generalization of this theorem for real reductive algebraic groups. More specifically, if…

Let $C$ be a hyperelliptic curve of genus $g\geq 3$. In this paper we give a new geometric description of the theta map for moduli spaces of rank 2 semistable vector bundles on $C$ with trivial determinant. In order to do this, we describe…

Let $L$ be a (semi)-positive line bundle over a Kahler manifold, $X$, fibered over a complex manifold $Y$. Assuming the fibers are compact and non-singular we prove that the hermitian vector bundle $E$ over $Y$ whose fibers over points $y$…

Gromov asked what a typical (finitely presented) group looks like, and he suggested a way to make the question precise in terms of limiting density. The typical finitely generated group is known to share some important properties with the…

A new global approach in the study of duality transformations is introduced. The geometrical structure of complex line bundles is generalized to higher order U(1) bundles which are classified by quantized charges and duality maps are…

We apply Ueda theory to a study of singular Hermitian metrics of a (strictly) nef line bundle $L$. Especially we study minimal singular metrics of $L$, metrics of $L$ with the mildest singularities among singular Hermitian metrics of $L$…

Let T be an algebraically bounded theory. We consider the $L(\bar\delta)$-expansions of T by a tuple $\bar \delta$ of derivations (which may be commuting or not). We investigate the model completion of either of the above theories, whose…

We prove a Torelli theorem for the moduli space of semistable parabolic Higgs bundles over a smooth complex projective algebraic curve under the assumption that the parabolic weight system is generic. When the genus is at least two, using…

In this paper, we introduce a new energy density function $\mathscr Y$ on the projective bundle $\mathbb{P}(T_M)\>M$ for a smooth map $f:(M,h)\>(N,g)$ between Riemannian manifolds $$\mathscr Y=g_{ij}f^i_\alpha f^j_\beta \frac{W^\alpha…

We introduce the concept of Bergman bundle attached to a hermitian manifold X, assuming the manifold X to be compact - although the results are local for a large part. The Bergman bundle is some sort of infinite dimensional very ample…

Zariski dense collections of quadratic points on curves $X$ are well-understood by results of Harris--Silverman and Vojta, but when $\dim X \geq 2$ there is not an analogous geometric characterization, even conjecturally. In this note we…

Given an open subset U of a projective curve Y and a smooth family f:V-->U of curves, with semi-stable reduction over Y, we show that for a sub variation of Hodge structures of rank >2 the Arakelov inequality must be strict. For families of…

Hermitian bundle gerbes with connection are geometric objects for which a notion of surface holonomy can be defined for closed oriented surfaces. We systematically introduce bundle gerbes by closing the pre-stack of trivial bundle gerbes…

In earlier work the authors proved the Bergman kernel expansion for semipositive line bundles over a Riemann surface whose curvature vanishes to atmost finite order at each point. Here we explore the related results and consequences of the…

We study Severi type inequalities for big line bundles on irregular varieties via cohomological rank functions. We show that these Severi type inequalities on an irregular variety $X$ are related to some natural defined birational…

Consider a positive Borel measure on a locally compact group. We define a notion of uniform density for such a measure, which is based on a group invariant introduced by Leptin in 1966. We then restrict to unimodular amenable groups and to…

An $F$-manifold is complex manifold with a multiplication on the holomorphic tangent bundle with a certain integrability condition. Important examples are Frobenius manifolds and especially base spaces of universal unfoldings of isolated…