The volume of pseudoeffective line bundles and partial equilibrium

Darvas, Tamás; Xia, Mingchen

doi:10.2140/gt.2024.28.1957

Geom. Topol.

2024

DOI: 10.2140/gt.2024.28.1957

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The volume of pseudoeffective line bundles and partial equilibrium

Tamás Darvas,

Mingchen Xia

Abstract: GT peer review and production are managed by EditFLOW ® from MSP.PUBLISHED BY mathematical sciences publishers nonprofit scientific publishing http://msp.org/

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2024

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Ding stability and Kähler–Einstein metrics on manifolds with big anticanonical class

Dervan,

Reboulet

2024

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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We introduce a notion of uniform Ding stability for a projective manifold with big anticanonical class, and prove that the existence of a unique Kähler–Einstein metric on such a manifold implies uniform Ding stability. The main new techniques are to develop a general theory of Deligne functionals – and corresponding slope formulas – for singular metrics, and to prove a slope formula for the Ding functional in the big setting. This extends work of Berman in the Fano situation, when the anticanonical class is actually ample, and proves one direction of the analogue of the Yau–Tian–Donaldson conjecture in this setting. We also speculate about the relevance of uniform Ding stability and K-stability to moduli in the big setting.

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Ding stability and Kähler–Einstein metrics on manifolds with big anticanonical class

Dervan,

Reboulet

2024

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

View full text Add to dashboard Cite

show abstract

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The volume of pseudoeffective line bundles and partial equilibrium

Abstract: GT peer review and production are managed by EditFLOW ® from MSP.PUBLISHED BY mathematical sciences publishers nonprofit scientific publishing http://msp.org/

Cited by 1 publication

References 54 publications

Ding stability and Kähler–Einstein metrics on manifolds with big anticanonical class

Ding stability and Kähler–Einstein metrics on manifolds with big anticanonical class

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