On boundedness and moduli spaces of K-stable Calabi-Yau fibrations over curves
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909644102828032 |
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| author | Hashizume, Kenta Hattori, Masafumi |
| author_facet | Hashizume, Kenta Hattori, Masafumi |
| contents | 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 [Hat22b] 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_01244 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On boundedness and moduli spaces of K-stable Calabi-Yau fibrations over curves Hashizume, Kenta Hattori, Masafumi Algebraic Geometry Differential Geometry 14J10 (Primary) 14J17, 14J27, 14J40 (Secondary) 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 [Hat22b] 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. |
| title | On boundedness and moduli spaces of K-stable Calabi-Yau fibrations over curves |
| topic | Algebraic Geometry Differential Geometry 14J10 (Primary) 14J17, 14J27, 14J40 (Secondary) |
| url | https://arxiv.org/abs/2305.01244 |