4 papers
Limiting Hodge Structures for Cubic Hypersurfaces of Secant Type
Renjie Lyu, Xuanyu Pan
The limiting Hodge structure relates the geometric degeneration of varieties to its Hodge-theoretic behavior. We study degenerations of cubic hypersurfaces whose singular central f…
The Chevalley--Weil formula for finite group actions on higher dimensional compact complex manifolds
Wenfei Liu, Renjie Lyu
Building on the Atiyah--Singer holomorphic Lefschetz fixed-point theorem, we define ramification modules associated to the fixed loci of a finite group acting on a compact complex…
Degenerations to secant cubic hypersurfaces and limiting Hodge structure
Renjie Lyu, Zhiwei Zheng
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 ingredie…
Lines on the secant cubic hypersurfaces of Severi varieties
Renjie Lyu
The secant varieties of Severi varieties provide special examples of (singular) cubic hypersurfaces. An interesting question asks when a given cubic hypersurface is projectively eq…