Sylow Criteria for Liftability of Automorphism Groups of Smooth Hypersurfaces

2026/07/26 by Baiting Xie, Zhiwei Zheng
#math.AG

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Abstract

In this paper, we first establish Sylow criteria for liftability of finite subgroups of the projective linear groups over arbitrary field. We also obtain Sylow criteria for F-liftability: if F is a nonsingular polynomial of degree d in N variables over a field of characteristic zero, then a finite subgroup G of Lin(F) is F-liftable if and only if for every prime p dividing gcd(|G|,N,d), there exists a Sylow p-subgroup of G that is F-liftable. Our proof combines restriction and corestriction in group cohomology with the reduction-to-Klein method.

Citations

• Automorphism groups of cubic fivefolds and fourfolds
• On the liftability of the automorphism group of smooth hypersurfaces of the projective space
• On Abelian Automorphism Groups of Hypersurfaces
• Automorphism groups of smooth quintic threefolds

Related

• On the liftability of the automorphism group of smooth hypersurfaces of the projective space
• Lifting finite groups of outer automorphisms of free groups, surface groups and their abelianizations
• Lifting Problem on Automorphism Groups of Cyclic Curves
• On Abelian Automorphism Groups of Hypersurfaces
• An obstruction to lifting to characteristic 0