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Weakly special test configurations of log canonical Fano varieties

Guodu Chen and Chuyu Zhou

Vol. 16 (2022), No. 10, 2415–2432
Abstract

Let (X,Δ) be a strictly lc log Fano pair, we show that every lc place of complements of (X,Δ) is dreamy and there exists a correspondence between weakly special test configurations of (X,Δ;KX Δ) and lc places of complements of (X,Δ).

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Keywords
lc Fano variety, weakly special test configuration, complement
Mathematical Subject Classification
Primary: 14J17
Secondary: 14J45
Milestones
Received: 25 July 2021
Revised: 4 January 2022
Accepted: 4 March 2022
Published: 28 January 2023
Authors
Guodu Chen
Institute for Theoretical Sciences
Westlake University
Hangzhou
Zheijang
China
Chuyu Zhou
Institute of Mathematics
École Polytechnique Fédérale de Lausanne (EPFL)
Lausanne
Switzerland