August 22, 2025Open Access

Special K-Stability and Positivity of CM Line Bundles

Puntos clave

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.

Resumen

We show that the CM line bundle on a proper family parametrizing specially K-stable varieties with maximal variation is big and nef. As an application, we show projectivity of any proper subspace of the coarse moduli space of uniformly adiabatically K-stable klt-trivial fibrations over curves constructed in Hashizume and Hattori (Geom. Topol. 29 (2025), 1619–1691).

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Cite This Study

Masafumi Hattori (Fri,) studied this question.

synapsesocial.com/papers/68af5231ad7bf08b1eada594 https://doi.org/https://doi.org/10.4171/prims/61-3-5