发表机构
Mathematical School of Science, Xiamen University; School of Mathematical Sciences, University of Chinese Academy of Sciences（厦门大学数学科学学院; 中国科学院大学数学科学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究退化到特定割线型奇异三次曲面的三次超曲面变形的极限霍奇结构，此前已研究过相关退化问题，此次继续探讨塞维里簇超平面截面的极限霍奇结构，其能联系簇的几何与霍奇理论退化。
AI 中文摘要
我们研究退化到特定割线型奇异三次曲面的三次超曲面变形的极限霍奇结构。Collino、Hassett和Laza研究了三次三维和四维的退化，其中心纤维分别是有理正规四次曲线和维罗纳曲面的割线簇。极限霍奇结构将簇的几何退化与霍奇理论退化联系起来。维罗纳曲面属于塞维里簇类，有理正规四次曲线是维罗纳曲面的超平面截面。我们之前研究了高维塞维里簇割线簇的类似退化问题。本文继续研究塞维里簇超平面截面的极限霍奇结构。
英文摘要
The limiting Hodge structure relates the geometric degeneration of varieties to its Hodge-theoretic behavior. We study degenerations of cubic hypersurfaces whose singular central fibers are secant cubics. The pertinent degenerations of cubic threefolds and fourfolds have been extensively studied for compactifying the associated moduli spaces. In the two cases, the secant cubics are constructed by the rational normal quartic and the Veronese surface, respectively. The Veronese surface is a Severi variety, and the rational normal quartic is a hyperplane section of it. In eariler work, we investigated degenerations to the secant cubics of higher-dimensional Severi varieties. Here we study the limiting Hodge structures for degenerations to their hyperplane sections.
Comments28 pages. Comments are welcome
