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PreprintCC BY 4.0arXiv

Density functions for filtrations of graded ideals

  • Suprajo Das
  • Hoang Le Truong
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{das2026density,
  title = {{Density functions for filtrations of graded ideals}},
  author = {Suprajo Das and Hoang Le Truong},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.18335},
  eprint = {2609.18335},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.18335},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Density functions for filtrations of graded ideals
AU  - Suprajo Das
AU  - Hoang Le Truong
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.18335
UR  - https://arxiv.org/abs/2609.18335
AB  - 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.
ER  -