The GIT-stability of Polarised Varieties via discrepancy
نویسنده
چکیده
We study the GIT stability of polarised varieities, in the language of the discrepancy of singularities, developed along the Mori Program. We give a new geometric numerical invariant of polarised varities, which is directly related to the discrepancy of singularities, whose negativity destabilises the polarised varieties. We relate this new invariant to the invariant which was used in J.Shah’s thorough analysis [Sh1], [Sh2] on the stability of the surface singularities. Also the Q-Gorenstein toric case are analysed.
منابع مشابه
On K-stability of Reductive Varieties
G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kähler metric of constant scalar curvature. In [Don02] Donaldson partially confirmed it in the case of projective toric varieties. In this paper we extend Donaldson’s results and computations to a new case, that of reductive varieties.
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