Abelian Automorphism Groups of Quartic Surfaces and Cubic Fourfolds

Tianzhen Peng; Zhiwei Zheng

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arXiv · 2106.14214

Abelian Automorphism Groups of Quartic Surfaces and Cubic Fourfolds

Tianzhen Peng·Zhiwei Zheng

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Abstract

In this paper, we develop a new method to classify abelian automorphism groups of hypersurfaces. We use this method to classify (Theorem 4.2) abelian groups that admit a liftable action on a smooth cubic fourfold. A parallel result (Theorem 5.1) is obtained for quartic surfaces.

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BibTeX RIS

Tianzhen Peng, Zhiwei Zheng. 2021-06-27. Abelian Automorphism Groups of Quartic Surfaces and Cubic Fourfolds. https://arxiv.org/abs/2106.14214

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