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Applications of the moduli continuity method to log K-stable pairs

Gallardo, Patricio and Martinez-Garcia, Jesus and Spotti, Cristiano (2020) 'Applications of the moduli continuity method to log K-stable pairs.' Journal of the London Mathematical Society. ISSN 0024-6107

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The 'moduli continuity method' permits an explicit algebraisation of the Gromov-Hausdorff compactification of Kähler-Einstein metrics on Fano manifolds in some fundamental examples. In this paper, we apply such method in the 'log setting' to describe explicitly some compact moduli spaces of K-polystable log Fano pairs. We focus on situations when the angle of singularities is perturbed in an interval sufficiently close to one, by considering constructions arising from Geometric Invariant Theory. More precisely, we discuss the cases of pairs given by cubic surfaces with anticanonical sections, and of projective space with non-Fano hypersurfaces, and we show ampleness of the CM line bundle on their good moduli space (in the sense of Alper). Finally, we introduce a conjecture relating K-stability (and degenerations) of log pairs formed by a fixed Fano variety and pluri-anticanonical sections to certain natural GIT quotients.

Item Type: Article
Uncontrolled Keywords: K-stability; Fano varieties; Kähler-Einstein; Geometric Invariant Theory
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 01 Oct 2020 12:39
Last Modified: 06 Jan 2022 14:18

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