Hilbert series and obstructions to asymptotic semistability
The first part of the survey deals with problems related to integral invariants for toric Fano manifolds. The second part deals with the definition of asymptotic Chow semistability. The basic results are given. In the third part is given the main result of this paper which claims that: ``Given a polarized manifold there are obstructions for asymptotic Chow semistability described as integral invariants which can be regarded as characters of the Lie algebra of holomorphic vector fields. In this paper we show that, on toric Fano manifolds the linear span of those Lie algebra characters coincides with the derivatives of the Laurent series of the Hilbert series.'' In sections 4,5 and 6 are also considered other problems. In the final section 7 the authors discusse the possible extension to general compact Sasaki manifolds. The bibliography contains 38 references. In summary this is an excellent paper.
Kähler metric of constant scalar curvature
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