An Oka principle for equivariant isomorphisms

Let G be a reductive complex Lie group acting holomorphically on normal Stein spaces X and Y, which are locally G-biholomorphic over a common categorical quotient Q. When is there a global G-biholomorphism X → Y? If the actions of G on X and Y are what we, with justification, call generic, we prove that the obstruction to solving this local-to-global problem is topological and provide sufficient conditions for it to vanish. Our main tool is the equivariant version of Grauert's Oka principle due to Heinzner and Kutzschebauch. We prove that X and Y are G-biholomorphic if X is K-contractible, where K is a maximal compact subgroup of G, or if X and Y are smooth and there is a G-diffeomorphism ψ : X → Y over Q, which is holomorphic when restricted to each fibre of the quotient map X → Q. We prove a similar theorem when ψ is only a G-homeomorphism, but with an assumption about its action on G-finite functions. When G is abelian, we obtain stronger theorems. Our results can be interpreted as instances of the Oka principle for sections of the sheaf of G-biholomorphisms from X to Y over Q. This sheaf can be badly singular, even for a low-dimensional representation of SL2(ℂ). Our work is in part motivated by the linearisation problem for actions on ℂn. It follows from one of our main results that a holomorphic G-action on ℂn, which is locally G-biholomorphic over a common quotient to a generic linear action, is linearisable.

The Principle of Common Concern and Climate Change

Effective policies combating global warming and incentivising reduction of greenhouse gases face fundamental collective action problems. States defending short term interests avoid international commitments and seek to benefit from measures combating global warming taken elsewhere. The paper explores the potential of Common Concern as an emerging principle of international law, in particular international environmental law, in addressing collective action problems and the global commons. It expounds the contours of the principle, its relationship to common heritage of mankind, to shared and differentiated responsibility and to public goods. It explores its potential to provide the foundations not only for international cooperation, but also to justify, and delimitate at the same time, unilateral action at home and deploying extraterritorial effects in addressing the challenges of global warming and climate change mitigation. As unilateral measures mainly translate into measures of trade policy, the principle of Common Concern is inherently linked and limited by existing legal disciplines in particular of the law of the World Trade Organization.