Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry, II

By Simon Donaldson, Song Sun. 2015

239 citations recorded by the source corpus.

In this paper we continue to study Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry. Our main focus is on the algebro-geometric meaning of Riemannian tangent cones and rescaled limits.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fa8d8abf7710b300cba40c2ae17052640139c0d6

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Gromov–Hausdorff limits of Kähler manifolds with Ricci curvature bounded below (2018, background): “1 of [18] (alternatively, Proposition 6.”
The partial $C^0$-estimate along the continuity method (2013, methodology): “We now review the construction in Donaldson-Sun [18] that we will need.”
On the Yau‐Tian‐Donaldson Conjecture for Singular Fano Varieties (2017, methodology): “Step 5 By adapting the arguments used in [35, 52, 23, 53, 14], one can show that as ti → 1, (X,ω(0,ti)) converges to a normal Q-Fano variety (X∞, d∞) with a Kähler-Einstein metric.”
Sasaki–Einstein metrics and K–stability (2015, methodology): “For Kähler-Einstein metrics in arbitrary dimension this estimate was obtained by Donaldson-Sun [40], using the Cheeger-Colding convergence theory [20] under Ricci curvature bounds, together with the Hörmander technique [51] for constructing holomorphic functions.”
Kähler–Einstein metrics along the smooth continuity method (2015, background): “We can choose a subsequence tk → T , such that Ftk(M) converges to a limit W ⊂ PN , and as shown in Donaldson-Sun [27], the partial C0-estimate implies, up to replacing m by a multiple, that W is a normal Q-Fano variety, homeomorphic to the Gromov-Hausdorff limit Z of the sequence (M,ωtk).”
Gromov-Hausdorff collapsing of Calabi-Yau manifolds (2013, result): “In the case of non-collapsing limits, analogous results about metric completions have been obtained in [25–27], and homeomorphism results have been obtained in [6] (see also [33]).”