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Title:
Openness of K-semistability for Fano varieties
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Abstract:
In this talk, I will explain the proof of openness of K-semistability for Fano varieties. This is one major step in the algebraic construction of Fano K-moduli spaces. We also establish a correspondence between weakly special test configurations and log canonical places of bounded complements. Our proof is a combination of valuative criteria for K-semistability due to Fujita and Li, boundedness of complements due to Birkar, and approximation techniques. This talk is based on joint work with Harold Blum and Chenyang Xu.
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