Métriques Kählériennes extrémales sur les surfaces toriques [d'après S. Donaldson]

Biquard, Olivier

Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1018, 21 p.

MR Zbl

@incollection{AST_2011__339__181_0,
     author = {Biquard, Olivier},
     title = {M\'etriques {K\"ahl\'eriennes} extr\'emales sur les surfaces toriques [d'apr\`es {S.} {Donaldson]}},
     booktitle = {S\'eminaire Bourbaki, volume 2009/2010, expos\'es 1012-1026},
     series = {Ast\'erisque},
     note = {talk:1018},
     pages = {181--201},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {339},
     year = {2011},
     mrnumber = {2906354},
     zbl = {1377.53090},
     language = {fr},
     url = {http://www.numdam.org/item/AST_2011__339__181_0/}
}

TY  - CHAP
AU  - Biquard, Olivier
TI  - Métriques Kählériennes extrémales sur les surfaces toriques [d'après S. Donaldson]
BT  - Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026
AU  - Collectif
T3  - Astérisque
N1  - talk:1018
PY  - 2011
SP  - 181
EP  - 201
IS  - 339
PB  - Société mathématique de France
UR  - http://www.numdam.org/item/AST_2011__339__181_0/
LA  - fr
ID  - AST_2011__339__181_0
ER  -

%0 Book Section
%A Biquard, Olivier
%T Métriques Kählériennes extrémales sur les surfaces toriques [d'après S. Donaldson]
%B Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026
%A Collectif
%S Astérisque
%Z talk:1018
%D 2011
%P 181-201
%N 339
%I Société mathématique de France
%U http://www.numdam.org/item/AST_2011__339__181_0/
%G fr
%F AST_2011__339__181_0

Biquard, Olivier. Métriques Kählériennes extrémales sur les surfaces toriques [d'après S. Donaldson], dans Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1018, 21 p. http://www.numdam.org/item/AST_2011__339__181_0/

Bibliographie
Cité par

[1] M. Abreu - Kähler geometry of toric varieties and extremal metrics, Internat. J. Math. 9 (1998), p. 641-651. | DOI | MR | Zbl

[2] V. Apostolov, D. M. J. Calderbank, P. Gauduchon & C. W. Tønnesen-Friedman - Hamiltonian $2$ -forms in Kähler geometry. III. Extremal metrics and stability, Invent. Math. 173 (2008), p. 547-601. | DOI | MR | Zbl

[3] C. Arezzo & F. Pacard - Blowing up and desingularizing constant scalar curvature Kähler manifolds, Acta Math. 196 (2006), p. 179-228. | DOI | MR | Zbl

[4] O. Biquard - Métriques kählériennes à courbure scalaire constante : unicité, stabilité, Séminaire Bourbaki, vol. 2004/2005, exp. n° 938, Astérisque 307 (2006), p. 1-31. | EuDML | Numdam | MR | Zbl

[5] E. Calabi - Extremal Kähler metrics, in Seminar on Differential Geometry, Ann. of Math. Stud., vol. 102, Princeton Univ. Press, 1982, p. 259-290. | MR | Zbl

[6] E. Calabi, Extremal Kähler metrics. II, in Differential geometry and complex analysis, Springer, 1985, p. 95-114. | DOI | MR | Zbl

[7] X. Chen - The space of Kähler metrics, J. Differential Geom. 56 (2000), p. 189-234. | DOI | MR | Zbl

[8] X. Chen & G. Tian - Geometry of Kähler metrics and foliations by holomorphic discs, Publ. Math. Inst. Hautes Études Sci. 107 (2008), p. 1-107. | DOI | EuDML | Numdam | MR | Zbl

[9] T. Delzant - Hamiltoniens périodiques et images convexes de l'application moment, Bull. Soc. Math. France 116 (1988), p. 315-339. | DOI | EuDML | Numdam | MR | Zbl

[10] S. K. Donaldson - Remarks on gauge theory, complex geometry and $4$ -manifold topology, in Fields Medallists' lectures, World Sci. Ser. 20th Century Math., vol. 5, World Sci. Publ., River Edge, NJ, 1997, p. 384-403. | DOI | MR

[11] S. K. Donaldson, Symmetric spaces, Kähler geometry and Hamiltonian dynamics, in Northern California Symplectic Geometry Seminar, Amer. Math. Soc. Transl. Ser. 2, vol. 196, Amer. Math. Soc., 1999, p. 13-33. | MR | Zbl

[12] S. K. Donaldson, Scalar Curvature and Projective Embeddings. I, J. Differential Geom. 59 (2001), p. 479-522. | DOI | MR | Zbl

[13] S. K. Donaldson, Scalar curvature and stability of toric varieties, J. Differential Geom. 62 (2002), p. 289-349. | DOI | MR | Zbl

[14] S. K. Donaldson, Interior estimates for solutions of Abreu's equation, Collect. Math. 56 (2005), p. 103-142. | EuDML | MR | Zbl

[15] S. K. Donaldson, Extremal metrics on toric surfaces : a continuity method, J. Differential Geom. 79 (2008), p. 389-432. | DOI | MR | Zbl

[16] S. K. Donaldson, Kähler geometry on toric manifolds, and some other manifolds with large symmetry, in Handbook of geometric analysis. No. 1, Adv. Lect. Math. (ALM), vol. 7, Int. Press, Somerville, MA, 2008, p. 29-75. | MR | Zbl

[17] S. K. Donaldson, Constant scalar curvature metrics on toric surfaces, Geom. Funct. Anal. 19 (2009), p. 83-136. | DOI | MR | Zbl

[18] D. Guan - On modified Mabuchi functional and Mabuchi moduli space of Kähler metrics on toric bundles, Math. Res. Lett. 6 (1999), p. 547-555. | DOI | MR | Zbl

[19] V. Guillemin - Kaehler structures on toric varieties, J. Differential Geom. 40 (1994), p. 285-309. | DOI | MR | Zbl

[20] V. Guillemin, Moment maps and combinatorial invariants of Hamiltonian $T^{n}$ -spaces, Progress in Math., vol. 122, Birkhäuser, 1994. | MR | Zbl

[21] T. Mabuchi - Uniqueness of extremal Kähler metrics for an integral Kähler class, Internat. J. Math. 15 (2004), p. 531-546. | DOI | MR | Zbl

[22] T. Mabuchi, An energy-theoretic approach to the Hitchin-Kobayashi correspondence for manifolds. I, Invent. Math. 159 (2005), p. 225-243. | DOI | MR | Zbl

[23] T. Mabuchi, $K$ -stability of constant scalar curvature polarization, prepublication arXiv :0812.4093.

[24] T. Mabuchi, A stronger concept of $K$ -stability, prepublication arXiv :0910.4617.

[25] J. Stoppa - $K$ -stability of constant scalar curvature Kähler manifolds, Adv. Math. 221 (2009), p. 1397-1408. | DOI | MR | Zbl

[26] G. Székelyhidi - Optimal test-configurations for toric varieties, J. Differential Geom. 80 (2008), p. 501-523. | DOI | MR | Zbl

[27] G. Tian - Kähler-Einstein metrics with positive scalar curvature, Invent. Math. 130 (1997), p. 1-37. | DOI | MR | Zbl

[28] N. S. Trudinger & X.-J. Wang - The affine Plateau problem, J. Amer. Math. Soc. 18 (2005), p. 253-289. | DOI | MR | Zbl

[29] X.-J. Wang & X. Zhu - Kähler-Ricci solitons on toric manifolds with positive first Chern class, Adv. Math. 188 (2004), p. 87-103. | DOI | MR | Zbl

[30] B. Zhou & X. Zhu - $K$ -stability on toric manifolds, Proc. Amer. Math. Soc. 136 (2008), p. 3301-3307. | DOI | MR | Zbl