分次理想的滤链的密度函数
Density functions for filtrations of graded ideals
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中文总结 AI 辅助
本文发展了标准分次整环上任意分次理想滤链的密度函数一般理论，证明其基本性质、分段多项式逼近与饱和密度函数的可微性，并给出符号幂与整闭包重合的数值判据及混合重数不等式。
中文摘要 AI 辅助
我们研究了标准分次整环中分次理想的滤链相关的密度函数。在扩展先前工作的基础上，我们为任意滤链发展了一般理论，并确立了其基本性质，包括存在性、连续性、对数凹性和积分表示。我们证明了每个密度函数都可以由截断的诺特滤链产生的分段多项式密度函数局部一致逼近。我们证明了饱和密度函数的可微性性质，并给出了多项式环中分次根理想的符号幂与其普通幂的整闭包何时重合的数值刻画。最后，我们建立了等生成理想的混合重数的若干不等式。
英文摘要
We study density functions associated with filtrations of graded ideals in standard graded domains. Extending earlier work, we develop a general theory for arbitrary filtrations and establish their fundamental properties, including existence, continuity, log-concavity, and integral representations. We show that every density function is locally uniformly approximable by piecewise polynomial density functions arising from truncated Noetherian filtrations. We prove differentiability properties of saturation density functions and give a numerical characterization of when the symbolic powers of a graded radical ideal in a polynomial ring coincide with the integral closures of its ordinary powers. Finally, we establish several inequalities for the mixed multiplicities of equigenerated ideals.
发表机构
- Ahmedabad University（艾哈迈达巴德大学）
- University of Engineering and Technology, Vietnam National University, Hanoi（越南国立大学河内工程技术大学）
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