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arXiv · 2506.10679

Equivariant CM minimization for extremal manifolds

Gabriel Frey
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Abstract

We prove an equivariant version of the CM minimization conjecture for extremal K\"ahler manifolds. This involves proving that, given an equivariant punctured family of polarized varieties, a relative version of the CM degree is strictly minimized by an extremal filling. This generalizes a result by Hattori for cscK manifolds with discrete automorphism group by allowing automorphisms and extremal metrics. As a main tool, we extend results by Sz\'ekelyhidi on asymptotic filtration Chow stability of cscK manifolds with discrete automorphism group to the extremal setting.

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Gabriel Frey. 2025-06-12. Equivariant CM minimization for extremal manifolds. https://arxiv.org/abs/2506.10679

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