Year: 2025
Type: preprint
Abstract: We prove an equivariant version of the CM minimization conjecture for extremal Kähler 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 Székelyhidi on asymptotic filtration Chow stability of cscK manifolds with discrete automorphism group to the extremal setting.
Source: arXiv (Cornell University)
Author: Frey, Gabriel
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417354689
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