Higher Bott-Chern forms and Beilinson's regulator

Bott-Chern Forms and Arithmetic Intersections

Let E : 0 → S → E → Q → 0 be a short exact sequence of hermitian vector bundles with metrics on S and Q induced from that on E. We compute the Bott-Chern form φ̃(E ) corresponding to any characteristic class φ, assuming E is projectively flat. The result is used to obtain a new presentation of the Arakelov Chow ring of the arithmetic Grassmannian.

On Bott–Chern forms and their applications

We use Chern–Weil theory for Hermitian holomorphic vector bundles with canonical connections for explicit computation of the Chern forms of trivial bundles with special non-diagonal Hermitian metrics. We prove that every ∂̄∂-exact real form of the type (k, k) on an n-dimensional complexmanifold X arises as a difference of the Chern character forms of trivial Hermitian vector bundles with canonic...

Analytic Cycles, Bott-chern Forms, and Singular Sets for the Yang-mills Flow on Kähler Manifolds

It is shown that the singular set for the Yang-Mills flow on unstable holomorphic vector bundles over compact Kähler manifolds is completely determined by the Harder-NarasimhanSeshadri filtration of the initial holomorphic bundle. We assign a multiplicity to irreducible top dimensional components of the singular set of a holomorphic bundle with a filtration by saturated subsheaves. We derive a ...

Relative Bott-Chern Secondary Characteristic Classes

In this paper, we introduce six axioms for relative Bott-Chern secondary characteristic classes and prove the uniqueness and existence theorem for them. Such a work provides us a natural way to understand and hence to prove the arithmetic Grothendieck-Riemann-Roch theorem.

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