Blowing up Kähler manifolds with constant scalar curvature. II.

DOI10.4007/annals.2009.170.685zbMath1202.53069arXivmath/0504115OpenAlexW2013964504MaRDI QIDQ731196

Frank Pacard, Claudio Arezzo

Publication date: 2 October 2009

Published in: Annals of Mathematics. Second Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504115

zbMATH Keywords

Kähler manifoldconstant scalar curvaturecomplex manifoldblowing up

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Kähler manifolds (32Q15) Special Riemannian manifolds (Einstein, Sasakian, etc.) (53C25)

Related Items (28)

RC-positivity and scalar-flat metrics on ruled surfaces ⋮ The Einstein-Maxwell equations and conformally Kähler geometry ⋮ Blowing up and desingularizing constant scalar curvature Kähler manifolds ⋮ Quantisation of extremal Kähler metrics ⋮ Slope instability of projective spaces blown up along a line ⋮ Smoothing singular constant scalar curvature Kähler surfaces and minimal Lagrangians ⋮ K-stability and parabolic stability ⋮ Geometric Constructions of Extremal Metrics on Complex Manifolds ⋮ Extremal metrics on the total space of destabilising test configurations ⋮ On holomorphic isometries into blow-ups of \(\mathbb{C}^n\) ⋮ Constant scalar curvature Kähler metrics on ramified Galois coverings ⋮ On blowing up extremal Kähler manifolds ⋮ A note on blow-ups of toric surfaces and csc Kähler metrics ⋮ Complete scalar-flat Kähler metrics on affine algebraic manifolds ⋮ Big and Nef Classes, Futaki Invariant and Resolutions of Cubic Threefolds ⋮ Expansions of solutions to extremal metric type equations on blowups of cscK surfaces ⋮ Unstable blowups ⋮ A smörgåsbord of scalar-flat Kähler ALE surfaces ⋮ On the Kummer construction for Kcsc metrics ⋮ Invariant scalar-flat Kähler metrics on \(\mathcal {O} (- \ell )\) ⋮ Extremal metrics on blowups ⋮ The Simanca metric admits a regular quantization ⋮ Critical metrics on connected sums of Einstein four-manifolds ⋮ Extremal K\"ahler metrics on blow-ups of parabolic ruled surfaces ⋮ On homothetic balanced metrics ⋮ Unstable polarized del Pezzo surfaces ⋮ Scalar curvature and asymptotic Chow stability of projective bundles and blowups ⋮ Blowing up extremal Kähler manifolds. II

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