Weakly special test configurations of log canonical Fano varieties

Chen, Guodu; Zhou, Chuyu

doi:10.2140/ant.2022.16.2415

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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

DOI: 10.2140/ant.2022.16.2415

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 $(X, Δ; - K_{X} - Δ)$ and lc places of complements of $(X, Δ)$ .

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

Vol. 16, No. 10, 2022