On boundedness and moduli spaces of K-stable Calabi–Yau fibrations over curves

Hashizume, Kenta¹ ; Hattori, Masafumi²

¹Department of Mathematics, Faculty of Science, Niigata University, Niigata, Japan
²Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, Japan

Geometry & topology, Tome 29 (2025) no. 3, pp. 1619-1691

Résumé

We show boundedness of polarized Calabi–Yau fibrations over curves only with fixed volumes of general fibers and Iitaka volumes. As its application, we construct a separated coarse moduli space of K-stable Calabi–Yau fibrations over curves in an adiabatic sense (Hattori 2022) and show that all members (resp. smooth members) of the moduli are simultaneously uniformly K-stable (resp. have cscK metrics) for a certain choice of polarizations.

Détail

DOI : 10.2140/gt.2025.29.1619

Keywords: klt-trivial fibration, K-stability, coarse moduli space

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