2022/06/25 by Lyu, Renjie, Zheng, Zhiwei
#14C30 #14D06 #14D07 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2206.12670
The secant variety of the Veronese surface is a singular cubic fourfold. The degeneration of Hodge structures of one-parameter degenerations to this secant cubic fourfold is a key ingredient for B.~Hassett and R.~Laza in studying the moduli space of cubic fourfolds via the period mapping. We generalize some of their results to the cubic hypersurface that is the secant variety of a Severi variety. Specifically, we study the limit mixed Hodge structures associated to one-parameter degenerations to the secant cubic hypersurface. Considering S.~Usui's partial compactification of a period domain for Hodge structures of general weights, we apply the limit mixed Hodge structure to characterize a local extension of the period map for the corresponding cubic hypersurfaces.