Kyoto Journal of Mathematics

Uniform K-stability and plt blowups of log Fano pairs

Kento Fujita

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Abstract

We show relationships between uniform K-stability and plt blowups of log Fano pairs. We see that it is enough to evaluate certain invariants defined by volume functions for all plt blowups in order to test the uniform K-stability of log Fano pairs. We also discuss the uniform K-stability of two log Fano pairs under crepant finite covers. Moreover, we give another proof of the K-semistability of the projective plane.

Article information

Source
Kyoto J. Math., Volume 59, Number 2 (2019), 399-418.

Dates
Received: 1 January 2017
Revised: 14 February 2017
Accepted: 9 March 2017
First available in Project Euclid: 19 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1555660964

Digital Object Identifier
doi:10.1215/21562261-2019-0012

Mathematical Reviews number (MathSciNet)
MR3960299

Zentralblatt MATH identifier
07080110

Subjects
Primary: 14J45: Fano varieties
Secondary: 14E30: Minimal model program (Mori theory, extremal rays)

Keywords
Fano varieties K-stability minimal model program

Citation

Fujita, Kento. Uniform K-stability and plt blowups of log Fano pairs. Kyoto J. Math. 59 (2019), no. 2, 399--418. doi:10.1215/21562261-2019-0012. https://projecteuclid.org/euclid.kjm/1555660964


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