## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Invariants of varieties and singularities inspired by Kähler-Einstein problems

Yuji Odaka

#### Abstract

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

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

Dates
First available in Project Euclid: 31 March 2015

https://projecteuclid.org/euclid.pja/1427806770

Digital Object Identifier
doi:10.3792/pjaa.91.50

Mathematical Reviews number (MathSciNet)
MR3327328

Zentralblatt MATH identifier
1338.14016

#### Citation

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. https://projecteuclid.org/euclid.pja/1427806770

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