Related papers: Bott-Chern Forms and Arithmetic Intersections

A equivalence relation, preserving the Chern-Weil form, is defined between connections on a complex vector bundle. Bundles equipped with such an equivalence class are called Structured Bundles, and their isomorphism classes form an abelian…

We study conditions under which sub-complexes of a double complex of vector spaces allow to compute the Bott-Chern cohomology. We are especially aimed at studying the Bott-Chern cohomology of special classes of solvmanifolds, namely,…

We consider a class of tautological top intersection products on the moduli space of stable pairs consisting of semistable vector bundles together with N sections on a smooth complex projective curve C. We show that when N is large, these…

An explicit formula for analytic torsion forms for fibrations by projective curves is given. In particular one obtains a formula for direct images in Arakelov geometry in the corresponding setting. The main tool is a new description of…

Using the concept of a cohesive module defined by Block, we use the theory of superconnections in the sense of Quillen to construct natural superconnections on Hermitian cohesive modules. By the Chern-Weil construction, we obtain…

In this paper we study the arithmetic invariants of Euclidean lattice in the context of Arakelov geometry. We regard a Euclidean lattice as a hermitian vector bundle $\bar E$ on ${\rm Spec}(\mathbb{Z})$ and consider two typical arithmetic…

A Bott manifold is a closed smooth manifold obtained as the total space of an iterated $\C P^1$-bundle starting with a point, where each $\C P^1$-bundle is the projectivization of a Whitney sum of two complex line bundles. A…

We provide an elementary proof of the Hartshorne-Serre correspondence for constructing vector bundles from local complete intersection subschemes of codimension two. This will be done, as in the correspondence of hypersurfaces and line…

In this short note we give an explicit presentation of the algebra A_n generated by the curvature 2-forms of the standard Hermitiam line bundles over SL_n/B as the quotient of the polynomial ring. The difference between A_n and H^*(SL_n/B)…

A fundamental goal of algebraic geometry is to do for singular varieties whatever we can do for smooth ones. Intersection homology, for example, directly produces groups associated to any variety which have almost all the properties of the…

We develop a theory of Cech-Bott-Chern cohomology and in this context we naturally come up with the relative Bott-Chern cohomology. In fact Bott-Chern cohomology has two relatives and they all arise from a single complex. Thus we study…

Let $\mathscr{V}\mathrm{ect}_n$ be the moduli stack of vector bundles of rank $n$ on schemes. We prove that, if $E$ is a Zariski sheaf of ring spectra which is equipped with finite quasi-smooth transfers and satisfies the projective bundle…

We develop a theory of arithmetic characteristic classes of (fully decomposed) automorphic vector bundles equipped with an invariant hermitian metric. These characteristic classes have values in an arithmetic Chow ring constructed by means…

In this article, we investigate an axiomatic approach introduced by Grivaux for the study of rational Bott-Chern cohomology, and use it in that context to define Chern classes of coherent sheaves. This method also allows us to derive a…

In a previous paper, we have defined arithmetic extension groups in the context of Arakelov geometry. In the present one, we introduce an arithmetic analogue of the Atiyah extension that defines an element -- the arithmetic Atiyah class --…

We study projectively flat holomorphic vector bundles over Riemann surfaces. To each such bundle, we naturally assign a Wronskian line bundle. The main idea is a notion of the division of two meromorphic sections. Abel's identity is…

Let $C$ be a smooth projective curve defined over the field of complex numbers. Let $E$ be a vector bundle on $C$, and fix an integer $d\geqslant 1$. Let $\mc Q:={\rm Quot}(E,d)$ be the Quot Scheme which parameterizes all torsion quotients…

A real Bott manifold is the total space of a sequence of $\R P^1$ bundles starting with a point, where each $\R P^1$ bundle is projectivization of a Whitney sum of two real line bundles. A real Bott manifold is a real toric manifold which…

We develop a theory of abstract arithmetic Chow rings where the role of the fibers at infinity is played by a complex of abelian groups that computes a suitable cohomology theory. This theory allows the construction of many variants of the…

We give a close formula for the N\'eron-Tate height of tautological integral cycles on Jacobians of curves over number fields as well as a new lower bound for the arithmetic self-intersection number $\hat{\omega}^2$ of the dualizing sheaf…