有限生成与不变喷子结构在非可约重参数化下的研究
Finite Generation and Structure of Invariant Jets under Non-Reductive Reparametrization
AI总结：
本文研究非可约重参数化群下喷代数的有限生成性，揭示其与Demailly-Semple塔的关联。
摘要：
我们研究复超曲率框架下的不变喷微分，重点在于非可约重参数化群$G_k = \mathbb{C}^{\ast} \ltimes U_k$的不变量代数。本文发展了一种统一的表示论和分层代数策略，用于$G_k$对$J_k\mathbb{C}^n$的$ρ$-作用，特别是确立了不变喷代数的有限生成性，这是Green-Griffiths-Demailly计划的核心。具体来说，我们证明了$\mathbb{C}^{\ast}$-分层的单菌体不变量$\mathbb{C}[J_k\mathbb{C}^n]^{U_k}$对于所有$n,k$都是有限生成的；等价地，不变喷微分的纤维环是一个有限生成的正分层$\mathbb{C}$-代数，因此其投影谱$\operatorname{Proj}\,\mathbb{C}[J_k\mathbb{C}^n]^{U_k}$存在且与Demailly-Semple塔一致。
英文摘要：
We study invariant jet differentials in the framework of complex hyperbolicity, focusing on the algebra of invariants for the non--reductive reparametrization group $G_k = \mathbb{C}^{\ast} \ltimes U_k$. The paper develops a uniform, representation--theoretic, and graded--algebraic strategy for the $ρ$--action of $G_k$ on $J_k\mathbb{C}^n$, establishing in particular the finite generation of the invariant jet algebra central to the Green--Griffiths--Demailly program. Specifically, we prove that the $\mathbb{C}^{\ast}$--graded algebra of unipotent invariants $\mathbb{C}[J_k\mathbb{C}^n]^{U_k}$ is finitely generated for all $n,k$; equivalently, the fiber ring of invariant jet differentials is a finitely generated positively graded $\mathbb{C}$--algebra, so that its projective spectrum $\operatorname{Proj}\,\mathbb{C}[J_k\mathbb{C}^n]^{U_k}$ exists and coincides with the Demailly--Semple tower.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
