Distortion and moment measure of non-archimedean psh metric

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• Eiji Inoue (RIKEN)
• Thursday 16 May 2024, 14:00-15:00
• Seminar Room 1, Newton Institute.

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EMGW04 - K-stability and moment maps

Intersection formula of Donaldson-Futaki invariant is crucial in Boucksom-Jonsson’s non-archimedean approach to K-stability: non-archimedean Monge-Ampere measure and energy pairing can describe intersection appearing in Donaldson-Futaki invariant.  In a study of optimal (K-)destabilization, we consider invariants which are expressed by higher equivariant intersection. Higher equivariant intersection of a test configuration \phi cannot be described by energy pairing of \phi. To describe this, I introduced non-archimedean moment measure. It is a measure on the product of Berkovich space and the real line whose marginals are non-archimedean Monge-Ampere measure and Duistermaat-Heckman measure.  In this talk, I newly introduce distortion of non-archimedean psh metric. It transforms a non-archimedean psh metric \phi to another non-archimedean psh metric Dist (\phi) by which we can reduce a certain integration with respect to moment measure of \phi to an integration with respect to NA Monge-Ampere measure of Dist (\phi). This enables us to express non-archimedean mu-entropy of \phi by Donaldson-Futaki invariant of Dist (\phi). 

This talk is part of the Isaac Newton Institute Seminar Series series.

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