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Automorphism groups of cubic fivefolds and fourfolds

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arxiv 2308.07186 v2 pith:DPETLA7G submitted 2023-08-14 math.AG

Song Yang , Xun Yu , Zigang Zhu This is my paper
classification math.AG
keywords groupscubicautomorphismfivefoldsfourfoldssmoothactingapplication
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In this paper, we introduce notions of partitionability and characteristic sets of homogeneous polynomials and give a complete classification of groups faithfully acting on smooth cubic fivefolds. Specifically, we prove that there exist 20 maximal ones among all such groups. As an application, we classify all possible subgroups of the automorphism groups of smooth cubic fourfolds.

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  1. Rational cubic fourfolds with a symplectic group of automorphisms

    math.AG 2025-09 conditional novelty 5.0 of 10

    Cubic fourfolds admitting a cyclic group of symplectic automorphisms of order not a power of 2 are rational and lie in the Hassett divisors C_14 or C_42.

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