A Guided Tour to Normalized Volume

DOI10.1007/978-3-030-34953-0_10zbMath1440.14015arXiv1806.07112OpenAlexW2809075290MaRDI QIDQ3300603

Yuchen Liu, Chi Li, Chen Yang Xu

Publication date: 29 July 2020

Published in: Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1806.07112

zbMATH Keywords

\(K\)-stabilitylocal volumesstable degeneration

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Global differential geometry of Hermitian and Kählerian manifolds (53C55) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Fano varieties (14J45) Minimal model program (Mori theory, extremal rays) (14E30) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35)

Related Items (17)

K-MODULI OF CURVES ON A QUADRIC SURFACE AND K3 SURFACES ⋮ The existence of the Kähler–Ricci soliton degeneration ⋮ On the stability of extensions of tangent sheaves on Kähler-Einstein Fano/Calabi-Yau pairs ⋮ Equivariant K-stability under finite group action ⋮ On the regularity of conical Calabi–Yau potentials ⋮ ACC for local volumes and boundedness of singularities ⋮ Algebraic uniqueness of Kähler-Ricci flow limits and optimal degenerations of Fano varieties ⋮ Canonical Kähler metrics and stability of algebraic varieties ⋮ On boundedness of singularities and minimal log discrepancies of Kollár components ⋮ Convexity of multiplicities of filtrations on local rings ⋮ K-stability and birational models of moduli of quartic \(K3\) surfaces ⋮ On positivity of the CM line bundle on K-moduli spaces ⋮ -SIGNATURE UNDER BIRATIONAL MORPHISMS ⋮ K-stability of Fano varieties: an algebro-geometric approach ⋮ On properness of K-moduli spaces and optimal degenerations of Fano varieties ⋮ Delta invariants of projective bundles and projective cones of Fano type ⋮ Optimal destabilization of K-unstable Fano varieties via stability thresholds

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