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On
boundedness and moduli spaces of K-stable Calabi–Yau
fibrations over curves
Kenta Hashizume and Masafumi Hattori |
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Geometry & Topology 29 (2025) 1619–1691
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Abstract |
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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. |
Keywords
klt-trivial fibration, K-stability, coarse moduli space
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Mathematical Subject Classification
Primary: 14J10
Secondary: 14J17, 14J27, 14J40
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References |
Publication
Received: 3 August 2023
Revised: 7 June 2024
Accepted: 27 July 2024
Published: 31 May 2025
Proposed: Mark Gross
Seconded: Dan Abramovich, Sándor J Kovács
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Authors |
| Kenta Hashizume | |
| Department of Mathematics Faculty of Science Niigata University Niigata Japan |
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| Masafumi Hattori | |
| Department of Mathematics Graduate School of Science Kyoto University Kyoto Japan |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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