Stability of pairs

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arxiv 1310.5544 v1 pith:MYSJ3KWO submitted 2013-10-21 math.DG

Gang Tian This is my paper · ORCID

classification math.DG

keywords pairsstabilityconnectiondiscussedessentiallyexpositoryk-stabilitynote

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This is essentially an expository note based on S. Paul's works on the stability of pairs. Its connection to K-stability will be also discussed.

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The constant scalar curvature K\"ahler condition is very general
math.AG 2025-04 reject novelty 6.0 of 10

Arc K-semistability is claimed to be a very general algebraic property in flat families via openness of Paul-stability of pairs, but the proof of the pair-stability lemma contains a false assertion about orbit-closure fibers.