Invariant uniformization

Uniformization and Anti-uniformization Properties of Ladder Systems

Let S denote a stationary subset of limit ordinals of ω1. A ladder system on S is a sequence {Lα : α ∈ S} such that each Lα is an unbounded subset of α of order type ω. A ladder system is uniformizable if for each sequence 〈fα : α ∈ S〉 of functions fα : Lα → ω there is an F : ω1 → ω such that F Lα =∗ fα for each α ∈ S. I.e., for each α ∈ S, {β ∈ Lα : F (β) 6= fα(β)} is finite. We now formulate ...

Uniformization of Rational Relations

Adaptive Uniformization: Technical Details

This paper discusses technical aspects related to adaptive uniformization [1]. We give the derivation of the schemes that we have used to compute the jump probabilities. We also give some more detailed results about the complexity of adaptive uniformization. This paper is not self contained, but is a supplement to [1]. A. P. A. van Moorsel has been supported by the Netherlands Organization for ...

Inseparable Local Uniformization

The aim of this paper is to prove that an algebraic variety over a field can be desingularized locally along a valuation after a purely inseparable alteration. Zariski was first to study the problem of desingularizing algebraic varieties along valuations. He called this problem local uniformization of valuations and observed that it should be considered as the local part of the desingularizatio...

Uniformization of Riemann Surfaces

The uniformization theorem states that every simply connected Riemann surface is conformally equivalent to the open unit disk, the complex plane, or the Riemann sphere. We present three aproaches to the uniformization of Riemann surfaces. We first prove the uniformization theorem via the construction of a harmonic function by the Dirichlet principle. We then give an alternate proof by triangula...