K-stability of Fano varieties: an algebro-geometric approach

DOI10.4171/EMSS/51zbMath1476.14030arXiv2011.10477OpenAlexW3198065228MaRDI QIDQ1983983

Chen Yang Xu

Publication date: 13 September 2021

Published in: EMS Surveys in Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.10477

zbMATH Keywords

Fano varietiesK-stabilityK-moduli

Mathematics Subject Classification ID

Algebraic moduli problems, moduli of vector bundles (14D20) Families, moduli, classification: algebraic theory (14J10) Fano varieties (14J45) Minimal model program (Mori theory, extremal rays) (14E30)

Related Items (23)

K-polystability of 3-dimensional log Fano pairs of Maeda type ⋮ Projective flatness over klt spaces and uniformisation of varieties with nef anti-canonical divisor ⋮ Finite generation for valuations computing stability thresholds and applications to K-stability ⋮ On deformation spaces of toric singularities and on singularities of K-moduli of Fano varieties ⋮ Seshadri constants and K-stability of Fano manifolds ⋮ K-stability of Fano threefolds of rank 4 and degree 24 ⋮ K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces ⋮ Stability conditions for polarised varieties ⋮ \(K\)-stability of Fano threefolds of rank 2 and degree 14 as double covers ⋮ Slope inequalities for KSB‐stable and K‐stable families ⋮ Cohomology of moduli space of cubic fourfolds. I ⋮ Canonical Kähler metrics and stability of algebraic varieties ⋮ Coregularity of Fano varieties ⋮ K-stable smooth Fano threefolds of Picard rank two ⋮ On K‐stability of some del Pezzo surfaces of Fano index 2 ⋮ New Sasaki–Einstein 5‐manifolds ⋮ A relative Yau-Tian-Donaldson conjecture and stability thresholds ⋮ Simply connected Sasaki-Einstein 5-manifolds: old and new ⋮ A 1-dimensional component of K-moduli of del Pezzo surfaces ⋮ Convexity of multiplicities of filtrations on local rings ⋮ K-stability and birational models of moduli of quartic \(K3\) surfaces ⋮ Cylinders in Fano varieties ⋮ Openness of K-semistability for Fano varieties

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