Abstract:The secant variety of the Veronese surface is a singular cubic fourfold. Degenerations to this specific cubic fourfold and the associated limiting Hodge structures are key ingredients for Hassett and Laza in studying the moduli space of cubic fourfolds and the period mapping. We generalize some results to the cubic hypersurfaces of secant type. Specifically, we compute the limit mixed Hodge structure for families of smooth cubic hypersurfaces degenerating to the cubic hypersurface of secant type. Using Usui's partial compactification and the resulting limit mixed Hodge structure, we characterize a local extension of the period map associated with the degenerating family.
| Comments: | 32 pages. Some sections has been revised. To appear in Algebraic Geometry |
| Subjects: | Algebraic Geometry (math.AG) |
| MSC classes: | 14C30, 14D05, 14D07, 32G20, 14N07 |
| Cite as: | arXiv:2206.12670 [math.AG] |
| (or arXiv:2206.12670v3 [math.AG] for this version) | |
| https://doi.org/10.48550/arXiv.2206.12670 arXiv-issued DOI via DataCite |
From: Renjie Lyu [view email]
[v1]
Sat, 25 Jun 2022 15:18:58 UTC (33 KB)
[v2]
Sun, 3 Jul 2022 04:46:11 UTC (34 KB)
[v3]
Mon, 25 May 2026 12:19:34 UTC (33 KB)
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