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Degenerating conic Kähler–Einstein metrics to the normal cone

Olivier Biquard and Henri Guenancia

Geometry & Topology 30 (2026) 247–306
Bibliography
1 M Abate, F Bracci, F Tovena, Embeddings of submanifolds and normal bundles, Adv. Math. 220 (2009) 620 MR2466428
2 R J Berman, S Boucksom, P Eyssidieux, V Guedj, A Zeriahi, Kähler–Einstein metrics and the Kähler–Ricci flow on log Fano varieties, J. Reine Angew. Math. 751 (2019) 27 MR3956691
3 R J Berman, S Boucksom, M Jonsson, A variational approach to the Yau–Tian–Donaldson conjecture, J. Amer. Math. Soc. 34 (2021) 605 MR4334189
4 B Berndtsson, A Brunn–Minkowski type inequality for Fano manifolds and some uniqueness theorems in Kähler geometry, Invent. Math. 200 (2015) 149 MR3323577
5 A L Besse, Einstein manifolds, 10, Springer (1987) MR867684
6 O Biquard, Métriques autoduales sur la boule, Invent. Math. 148 (2002) 545 MR1908060
7 O Biquard, Métriques hyperkählériennes pliées, Bull. Soc. Math. France 147 (2019) 303 MR3982279
8 O Biquard, H Guenancia, Degenerating Kähler–Einstein cones, locally symmetric cusps, and the Tian-Yau metric, Invent. Math. 230 (2022) 1101 MR4506773
9 O Biquard, H J Hein, The renormalized volume of a 4-dimensional Ricci-flat ALE space, J. Differential Geom. 123 (2023) 411 MR4584857
10 O Biquard, V Minerbe, A Kummer construction for gravitational instantons, Comm. Math. Phys. 308 (2011) 773 MR2855540
11 A Blanchard, Sur les variétés analytiques complexes, Ann. Sci. École Norm. Sup. (3) 73 (1956) 157 MR87184
12 S Brendle, Ricci flat Kähler metrics with edge singularities, Int. Math. Res. Not. 2013 (2013) 5727 MR3144178
13 I A Cheltsov, Y A Rubinstein, On flops and canonical metrics, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 18 (2018) 283 MR3783790
14 X Chen, S Donaldson, S Sun, Kähler–Einstein metrics and stability, Int. Math. Res. Not. 2014 (2014) 2119 MR3194014
15 R J Conlon, H J Hein, Asymptotically conical Calabi–Yau manifolds, I, Duke Math. J. 162 (2013) 2855 MR3161306
16 T Darvas, Y A Rubinstein, Tian’s properness conjectures and Finsler geometry of the space of Kähler metrics, J. Amer. Math. Soc. 30 (2017) 347 MR3600039
17 T Delcroix, K-stability of Fano spherical varieties, Ann. Sci. Éc. Norm. Supér. (4) 53 (2020) 615 MR4118525
18 T Delcroix, Limits of conical Kähler–Einstein metrics on rank one horosymmetric spaces, Bull. Lond. Math. Soc. 56 (2024) 2514 MR4780714
19 S K Donaldson, Kähler metrics with cone singularities along a divisor, from: "Essays in mathematics and its applications" (editors P M Pardalos, T M Rassias), Springer (2012) 49 MR2975584
20 K Fujita, On log K-stability for asymptotically log Fano varieties, Ann. Fac. Sci. Toulouse Math. (6) 25 (2016) 1013 MR3582118
21 H Guenancia, Kähler–Einstein metrics : from cones to cusps, J. Reine Angew. Math. 759 (2020) 1 MR4058174
22 H Guenancia, M Păun, Conic singularities metrics with prescribed Ricci curvature : general cone angles along normal crossing divisors, J. Differential Geom. 103 (2016) 15 MR3488129
23 Y Hashimoto, Scalar curvature and Futaki invariant of Kähler metrics with cone singularities along a divisor, Ann. Inst. Fourier (Grenoble) 69 (2019) 591 MR3978320
24 P Jahnke, Submanifolds with splitting tangent sequence, Math. Z. 251 (2005) 491 MR2190340
25 T Jeffres, R Mazzeo, Y A Rubinstein, Kähler–Einstein metrics with edge singularities, Ann. of Math. (2) 183 (2016) 95 MR3432582
26 D D Joyce, Compact manifolds with special holonomy, Oxford Univ. Press (2000) MR1787733
27 C Li, Numerical solutions of Kähler–Einstein metrics on 2 with conical singularities along a smooth quadric curve, J. Geom. Anal. 25 (2015) 1773 MR3358073
28 C Li, On sharp rates and analytic compactifications of asymptotically conical Kähler metrics, Duke Math. J. 169 (2020) 1397 MR4101736
29 C Li, G-uniform stability and Kähler–Einstein metrics on Fano varieties, Invent. Math. 227 (2022) 661 MR4372222
30 C Li, S Sun, Conical Kähler–Einstein metrics revisited, Comm. Math. Phys. 331 (2014) 927 MR3248054
31 H Matsumura, P Monsky, On the automorphisms of hypersurfaces, J. Math. Kyoto Univ. 3 (1963/64) 347 MR168559
32 Y Matsushima, Sur la structure du groupe d’homéomorphismes analytiques d’une certaine variété kählérienne, Nagoya Math. J. 11 (1957) 145 MR94478
33 S Mori, Projective manifolds with ample tangent bundles, Ann. of Math. (2) 110 (1979) 593 MR554387
34 T Oda, Convex bodies and algebraic geometry : an introduction to the theory of toric varieties, 15, Springer (1988) MR922894
35 Y A Rubinstein, K Zhang, Angle deformation of Kähler–Einstein edge metrics on Hirzebruch surfaces, Pure Appl. Math. Q. 18 (2022) 343 MR4381856
36 Y T Siu, S T Yau, Compact Kähler manifolds of positive bisectional curvature, Invent. Math. 59 (1980) 189 MR577360
37 D M Snow, Cohomology of twisted holomorphic forms on Grassmann manifolds and quadric hypersurfaces, Math. Ann. 276 (1986) 159 MR863714
38 G Székelyhidi, A remark on conical Kähler–Einstein metrics, Math. Res. Lett. 20 (2013) 581 MR3162849
39 G Tian, On Kähler–Einstein metrics on certain Kähler manifolds with C1(M) > 0, Invent. Math. 89 (1987) 225 MR894378
40 G Tian, S T Yau, Complete Kähler manifolds with zero Ricci curvature, II, Invent. Math. 106 (1991) 27 MR1123371
41 A van de Ven, A property of algebraic varieties in complex projective spaces, from: "Colloque Géom. Diff. Globale", Librairie Universitaire (1959) 151 MR116361
42 J M Wahl, A cohomological characterization of n, Invent. Math. 72 (1983) 315 MR700774