Finiteness of K-moduli compactifications under the boundedness of K-semistable degenerations

Abstract

In this note, we prove the finite semi-algebraic chamber decomposition theorem for K-semi(poly)stability under the assumption of the log boundedness of K-semistable degenerations. This boundedness assumption is inspired by the expected finiteness of K-moduli compactifications.

arXiv comment26 pages, Final version, accepted by Sci.China Math. Title changed, main body largely revised according to the referee's comments and suggestions