Abelian Automorphism Groups of Quartic Surfaces and Cubic Fourfolds

Published 27 Jun 2021 in math.AG | (2106.14214v2)

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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