Open Access
April 2015 Invariants of varieties and singularities inspired by Kähler-Einstein problems
Yuji Odaka
Proc. Japan Acad. Ser. A Math. Sci. 91(4): 50-55 (April 2015). DOI: 10.3792/pjaa.91.50

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.

Citation

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Yuji Odaka. "Invariants of varieties and singularities inspired by Kähler-Einstein problems." Proc. Japan Acad. Ser. A Math. Sci. 91 (4) 50 - 55, April 2015. https://doi.org/10.3792/pjaa.91.50

Information

Published: April 2015
First available in Project Euclid: 31 March 2015

zbMATH: 1338.14016
MathSciNet: MR3327328
Digital Object Identifier: 10.3792/pjaa.91.50

Subjects:
Primary: 14E30
Secondary: 14B05 , 32Q15

Keywords: intersection number , K-stability , minimal model program

Rights: Copyright © 2015 The Japan Academy

Vol.91 • No. 4 • April 2015
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