Rigidity of Graded Integral Domains and of their Veronese Subrings

2023/08/09 by Daniel Daigle, Daigle, Daniel · 1 citation
Mathematics · #14R05 #14R20. Secondary: 14C20 #14R25 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 13N15

paper · doi:10.48550/arxiv.2308.05066

Abstract

A ring R is said to be rigid if the only locally nilpotent derivation of R is the zero derivation. Let G be an abelian group, and B = (direct sum of B_i for i in G) be a G-graded commutative integral domain of characteristic 0. For each subgroup H of G, consider the Veronese subring B(H) of B, defined by B(H) = (direct sum of the B_i for i in H). We study the following questions. If B is non-rigid, does it follow that B(H) is non-rigid? Can derivations of B(H) be extended to derivations of B? What are the properties of the set of subgroups H of G such that B(H) is non-rigid?

Citations

• Actions of SL2(k) on Affine k-Domains and Fundamental Pairs
• Locally Nilpotent Derivations of Graded Integral Domains and Cylindricity
• \mathbbmG_a-ACTIONS ON THE COMPLEMENTS OF HYPERSURFACES
• Locally nilpotent derivations and the structure of rings
• Ga-ACTIONS ON AFFINE CONES
• Homogeneous locally nilpotent derivations of k[X, Y, Z]

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• The Rigid Pham-Brieskorn Threefolds

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