Finite Generation and Structure of Invariant Jets under Non-Reductive Reparametrization

2020/12/12 by Rahmati, Mohammad Reza
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2012.08310

Abstract

We study invariant jet differentials in the framework of complex hyperbolicity, focusing on the algebra of invariants for the non--reductive reparametrization group G_k = ℂ^∗ \ltimes U_k. The paper develops a uniform, representation--theoretic, and graded--algebraic strategy for the ρ--action of G_k on J_kℂⁿ, establishing in particular the finite generation of the invariant jet algebra central to the Green--Griffiths--Demailly program. Specifically, we prove that the ℂ^∗--graded algebra of unipotent invariants ℂ[J_kℂⁿ]^U_k is finitely generated for all n,k; equivalently, the fiber ring of invariant jet differentials is a finitely generated positively graded ℂ--algebra, so that its projective spectrum Proj ℂ[J_kℂⁿ]^U_k exists and coincides with the Demailly--Semple tower.

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