This article is cited in 4 papers

Towards finite generation of higher rational rank valuations

C. Xu<sup>abc

a</sup> Department of Mathematics, Princeton University, Princeton, NJ, USA
^b Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, USA
^c Beijing International Center for Mathematical Research, Peking University, Beijing, P.R. China

Abstract: We propose a finite generation conjecture for the valuation which computes the stability threshold of a log Fano pair. We also initiate a degeneration strategy for attacking the conjecture.
Bibliography: 17 titles.

Keywords: log Fano pair, $\mathrm{K}$-stability, $\mathbb Q$-complement, degeneration.

UDC: 512.725+512.761+512.765

MSC: Primary 14B05; Secondary 14E30

Received: 19.05.2020 and 09.10.2020

DOI: 10.4213/sm9448

 English version: Sbornik: Mathematics, 2021, 212:3, 416–432

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