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August 22, 2025Publications of the Research Institute for Mathematical Sciences0 citationsOpen Access

Special K-Stability and Positivity of CM Line Bundles

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MHMasafumi Hattori

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.

Abstract

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 (2025) studied this question.

synapsesocial.com/papers/68af5231ad7bf08b1eada594https://doi.org/10.4171/prims/61-3-5
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