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Uniqueness of equivariant singular Bott-Chern classes

Shun Tang (2012)

Annales de l’institut Fourier

In this paper, we shall discuss possible theories of defining equivariant singular Bott-Chern classes and corresponding uniqueness property. By adding a natural axiomatic characterization to the usual ones of equivariant Bott-Chern secondary characteristic classes, we will see that the construction of Bismut’s equivariant Bott-Chern singular currents provides a unique way to define a theory of equivariant singular Bott-Chern classes. This generalizes J. I. Burgos Gil and R. Liţcanu’s discussion...

Uniqueness of Kähler-Einstein cone metrics.

Thalia D. Jeffres (2000)

Publicacions Matemàtiques

The purpose of this paper is to describe a method to construct a Kähler metric with cone singularity along a divisor and to illustrate a type of maximum principle for these incomplete metrics by showing that Kähler-Einstein metrics are unique in geometric Hölder spaces.

Uniqueness problem for meromorphic mappings with truncated multiplicities and few targets

Gerd Dethloff, Tran Van Tan (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper, using techniques of value distribution theory, we give a uniqueness theorem for meromorphic mappings of ℂ m into ℂ P n with truncated multiplicities and “few" targets. We also give a theorem of linear degeneration for such maps with truncated multiplicities and moving targets.

Universal divisors in Hardy spaces

E. Amar, C. Menini (2000)

Studia Mathematica

We study a division problem in the Hardy classes H p ( ) of the unit ball of ℂ 2 which generalizes the H p corona problem, the generators being allowed to have common zeros. MPrecisely, if S is a subset of , we study conditions on a ℂ k -valued bounded Mholomorphic function B, with B | S = 0 , in order that for 1 ≤ p < ∞ and any function f ∈ H p ( ) with f | S = 0 there is a ℂ k -valued H p ( ) holomorphic function F with f = B·F, i.e. the module generated by the components of B in the Hardy class H p ( ) is the entire module M S : = f ∈ H p ( ) : f | S = 0 . As a special case,...

Universal isomonodromic deformations of meromorphic rank 2 connections on curves

Viktoria Heu (2010)

Annales de l’institut Fourier

We consider tracefree meromorphic rank 2 connections over compact Riemann surfaces of arbitrary genus. By deforming the curve, the position of the poles and the connection, we construct the global universal isomonodromic deformation of such a connection. Our construction, which is specific to the tracefree rank 2 case, does not need any Stokes analysis for irregular singularities. It is thereby more elementary than the construction in arbitrary rank due to B. Malgrange and I. Krichever and it includes...

Universal reparametrization of a family of cycles : a new approach to meromorphic equivalence relations

David Mathieu (2000)

Annales de l'institut Fourier

We study analytic families of non-compact cycles, and prove there exists an analytic space of finite dimension, which gives a universal reparametrization of such a family, under some assumptions of regularity. Then we prove an analogous statement for meromorphic families of non-compact cycles. That is a new approach to Grauert’s results about meromorphic equivalence relations.

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