Special K-Stability and Positivity of CM Line Bundles

Key Points

• The CM line bundle on specially K-stable varieties is shown to be big and nef, supporting its geometrical properties.
• This finding implies projectivity for proper subspaces in the coarse moduli space, with application in algebraic geometry.
• Analysis focuses on uniformly adiabatically K-stable klt-trivial fibrations over curves, derived from established work by Hashizume and Hattori.
• Previous constructions regarding moduli spaces are validated by demonstrating the relationship between special k-stability and CM line bundles.