发表机构
University of Miami; Univ. Grenoble Alpes（迈阿密大学; 格勒诺布尔阿尔卑斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明特征零代数闭域上所有光滑四次双n重（n≥2）在格罗莫夫意义下代数椭圆，特别回答四次双立体情形的问题4.28，并证明移除余维数至少二的闭子集保持该性质。
AI 中文摘要
我们证明，在特征零的代数闭域上，每个光滑的四次双n-重（n≥2）在格罗莫夫意义下都是代数椭圆的。特别地，每个光滑的四次双立体是代数椭圆的，这回答了[M. Zaidenberg, Algebraic Gromov ellipticity: a brief survey, Taiwanese J. Math. 29 (2025), no. 6, 1681-1705]中的问题4.28。我们还证明了，对于光滑的四次双空间和维数至少为二的光滑三次超曲面，移除任何余维数至少为二的闭子集保持代数椭圆性。
英文摘要
We prove that every smooth quartic double $n$-fold, $n\ge2$, over an algebraically closed field of characteristic zero is algebraically elliptic in Gromov's sense. In particular, every smooth quartic double solid is algebraically elliptic, which answers Question~4.28 in [M. Zaidenberg, Algebraic Gromov ellipticity: a brief survey, Taiwanese J. Math. 29 (2025), no. 6, 1681-1705]. We also prove that removing any closed subset of codimension at least two preserves algebraic ellipticity for smooth quartic double spaces and smooth cubic hypersurfaces of dimension at least two.
Comments15 pages
