Curvature and relative volume forms
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866910909005299712 |
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| author | Rizzi, Luca Zucconi, Francesco |
| author_facet | Rizzi, Luca Zucconi, Francesco |
| contents | Using metric techniques introduced by Berndtsson, we show a result on constancy of families dominated by a constant variety and, on the opposite side, a result on the strong non isotriviality of certain families of surfaces with positive index. We also give metric interpretations of liftability of relative volume forms and of strong non isotriviality in terms of the complex conjugate of a suitable representative of the Kodaira-Spencer class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08218 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Curvature and relative volume forms Rizzi, Luca Zucconi, Francesco Algebraic Geometry Using metric techniques introduced by Berndtsson, we show a result on constancy of families dominated by a constant variety and, on the opposite side, a result on the strong non isotriviality of certain families of surfaces with positive index. We also give metric interpretations of liftability of relative volume forms and of strong non isotriviality in terms of the complex conjugate of a suitable representative of the Kodaira-Spencer class. |
| title | Curvature and relative volume forms |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.08218 |