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PreprintCC BY 4.0arXiv

Symbolic Powers and Asymptotic Invariants of GL-Invariant Ideals

  • Sankhaneel Bisui
  • Alexandra Seceleanu
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Abstract

This work concerns ideals invariant under the action of the group of linear base changes on a generic matrix; we call these GL-invariant ideals. We determine the ordinary powers, their saturations with respect to determinantal ideals, and the symbolic powers of GL-invariant ideals. We give explicit formulas for asymptotic invariants known as (skew) Waldschmidt constants and asymptotic resurgence, which measure the growth of these families and compare the ordinary and symbolic topologies. We also prove that the generalized symbolic Rees algebras associated with these ideals are Noetherian.

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Cite

BibTeXRIS
BibTeX
@misc{bisui2026symbolic,
  title = {{Symbolic Powers and Asymptotic Invariants of GL-Invariant Ideals}},
  author = {Sankhaneel Bisui and Alexandra Seceleanu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03131},
  eprint = {2609.03131},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03131},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Symbolic Powers and Asymptotic Invariants of GL-Invariant Ideals
AU  - Sankhaneel Bisui
AU  - Alexandra Seceleanu
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.03131
UR  - https://arxiv.org/abs/2609.03131
AB  - This work concerns ideals invariant under the action of the group of linear base changes on a generic matrix; we call these GL-invariant ideals. We determine the ordinary powers, their saturations with respect to determinantal ideals, and the symbolic powers of GL-invariant ideals. We give explicit formulas for asymptotic invariants known as (skew) Waldschmidt constants and asymptotic resurgence, which measure the growth of these families and compare the ordinary and symbolic topologies. We also prove that the generalized symbolic Rees algebras associated with these ideals are Noetherian.
ER  -