The Calabi Conjecture and K-stability

DOI10.1093/imrn/rnr107zbMath1484.32043arXiv1010.3597OpenAlexW1978132516WikidataQ122900881 ScholiaQ122900881MaRDI QIDQ2889566

Yuji Odaka

Publication date: 8 June 2012

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1010.3597

zbMATH Keywords

stabilityCalabi-Yau varieties

Mathematics Subject Classification ID

Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Calabi-Yau theory (complex-analytic aspects) (32Q25) Notions of stability for complex manifolds (32Q26)

Related Items (21)

K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES ⋮ Geodesic rays and stability in the lowercase cscK problem ⋮ Canonical Kähler metrics and arithmetics: generalizing Faltings heights ⋮ On K-stability of finite covers ⋮ Positivity of the CM line bundle for families of \(K\)-stable klt Fano varieties ⋮ Relative algebro-geometric stabilities of toric manifolds ⋮ Note on \(K\)-stability of pairs ⋮ Openness results for uniform K-stability ⋮ Uniform \(K\)-stability, Duistermaat-Heckman measures and singularities of pairs ⋮ Alpha invariant and K-stability of \(\mathbb Q\)-Fano varieties ⋮ Tropical Geometric Compactification of Moduli, I – M g Case ⋮ The GIT stability of polarized varieties via discrepancy ⋮ A generalization of the Ross-Thomas slope theory ⋮ Valuative stability of polarised varieties ⋮ Nonexistence of asymptotic GIT compactification ⋮ Kähler-Einstein metrics on stable varieties and log canonical pairs ⋮ K-stability of Fano varieties: an algebro-geometric approach ⋮ Testing log K-stability by blowing up formalism ⋮ Stable maps in higher dimensions ⋮ Stability of valuations and Kollár components ⋮ Degenerated Calabi-Yau varieties with infinite components, moduli compactifications, and limit toroidal structures

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