Stoppa:



  <1> Lightning review of Kaehler geometry. Calabi's functional and the problem of constant scalar curvature for smooth projective varieties. The algebro-geometric notion of K-semistability. [1,7]
<2,3> Moment maps, Bergman kernels, and Donaldson's proof of a lower bound for the Calabi functional in terms K-semistability. [2]
<4,5> Some improvements on Donaldson's result (stronger algebro-geometric stability notions for constant scalar curvature and extremal Kaehler metrics). [3,4,5,6]

References:


[1] S. Donaldson, "Scalar curvature and stability of toric varieties", J. Differential Geom. 62 (2002), no. 2, 289-349;
[2] S. Donaldson, "Lower bounds on the Calabi functional", J. Differential Geom. 70 (2005), no. 3, 453-472 (arXiv:math/0506501);
[3] S. Donaldson, "b-Stability and Blow-Ups", Proc. Edinb. Math. Soc. (2) 57 (2014), no. 1, 125-137 (arXiv:1107.1699);
[4] J. Stoppa, "K-stability of constant scalar curvature Kaehler manifolds", Adv. Math. 221 (2009), no. 4, 1397-1408 (arXiv:1111.5826v1);
[5] J. Stoppa, G. Szekelyhidi, "Relative K-stability of extremal metrics", JEMS 13 (2011), no. 4, 899-909; (arXiv:0912.4095);
[6] G. Szekelyhidi, "Filtrations and test-configurations", (with an appendix by S. Boucksom); (arxiv:1111.498);
[7] G. Szekelyhidi, "Introduction to Extremal metrics".