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• W3200014914 endingPage "2697" @default.
• W3200014914 startingPage "2643" @default.
• W3200014914 abstract "K-polystability is, on the one hand, conjecturally equivalent to the existence of certain canonical Kahler metrics on polarised varieties, and, on the other hand, conjecturally gives the correct notion to form moduli. We introduce a notion of stability for families of K-polystable varieties, extending the classical notion of slope stability of a bundle, viewed as a family of K-polystable varieties via the associated projectivisation. We conjecture that this is the correct condition for forming moduli of fibrations. Our main result relates this stability condition to Kahler geometry: we prove that the existence of an optimal symplectic connection implies semistability of the fibration. An optimal symplectic connection is a choice of fibrewise constant scalar curvature Kahler metric, satisfying a certain geometric partial differential equation. We conjecture that the existence of such a connection is equivalent to polystability of the fibration. We prove a finite dimensional analogue of this conjecture, by describing a GIT problem for fibrations embedded in a fixed projective space, and showing that GIT polystability is equivalent to the existence of a zero of a certain moment map." @default.
• W3200014914 created "2021-09-27" @default.
• W3200014914 creator A5020993951 @default.
• W3200014914 creator A5070389295 @default.
• W3200014914 date "2021-09-03" @default.
• W3200014914 modified "2023-09-23" @default.
• W3200014914 title "Moduli theory, stability of fibrations and optimal symplectic connections" @default.
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• W3200014914 doi "https://doi.org/10.2140/gt.2021.25.2643" @default.
• W3200014914 hasPublicationYear "2021" @default.
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