Proceedings of the Japan Academy, Series A, Mathematical Sciences

Invariants of varieties and singularities inspired by Kähler-Einstein problems

Yuji Odaka

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We extend the framework of K-stability~[30],~[8] to a more general algebro-geometric setting, such as partial desingularisations of fixed singularities, (not necessarily flat) families over higher dimensional base and birational geometry of surfaces.

We also observe that “concavity” of the volume function implies decrease of the (generalised) Donaldson–Futaki invariants along the Minimal Model Program, in our generalised settings. Several related results on the connection with the MMP theory, some of which are new even in the original setting of families over curves, are also proved.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 91, Number 4 (2015), 50-55.

First available in Project Euclid: 31 March 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14E30: Minimal model program (Mori theory, extremal rays)
Secondary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 32Q15: Kähler manifolds

Intersection number Minimal Model Program K-stability


Odaka, Yuji. Invariants of varieties and singularities inspired by Kähler-Einstein problems. Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), no. 4, 50--55. doi:10.3792/pjaa.91.50.

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