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PreprintCC BY 4.0arXiv

The Waldschmidt constant of square-free principal Borel ideals

  • Ajay Kumar
  • Rajiv Kumar
  • Paramhans Kushwaha
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Abstract

Fix a square-free monomial m = xi1 ⋯ xis in S = K[x1, …, xn], where K is a field. The ideal generated by all square-free monomials that are Borel moves of m is referred to as the \emph{square-free principal Borel ideal}, denoted by sfBorel(m). While the Waldschmidt constant of sfBorel(m) has been partially studied in the literature, we consider the remaining cases and provide bounds for the Waldschmidt constant of sfBorel(m). In some cases, we explicitly compute its exact value. Furthermore, we study this invariant for square-free Borel and square-free lex-segment ideals, establishing both bounds and exact values for special cases.

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Cite

BibTeXRIS
BibTeX
@misc{kumar2026waldschmidt,
  title = {{The Waldschmidt constant of square-free principal Borel ideals}},
  author = {Ajay Kumar and Rajiv Kumar and Paramhans Kushwaha},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.32524},
  eprint = {2609.32524},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.32524},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Waldschmidt constant of square-free principal Borel ideals
AU  - Ajay Kumar
AU  - Rajiv Kumar
AU  - Paramhans Kushwaha
PY  - 2026
DA  - 2026/09/26
PB  - arXiv
DO  - 10.48550/arxiv.2609.32524
UR  - https://arxiv.org/abs/2609.32524
AB  - Fix a square-free monomial m = x_i_1 ⋯ x_i_s in S = K[x_1, …, x_n], where K is a field. The ideal generated by all square-free monomials that are Borel moves of m is referred to as the \emph{square-free principal Borel ideal}, denoted by sfBorel(m). While the Waldschmidt constant of sfBorel(m) has been partially studied in the literature, we consider the remaining cases and provide bounds for the Waldschmidt constant of sfBorel(m). In some cases, we explicitly compute its exact value. Furthermore, we study this invariant for square-free Borel and square-free lex-segment ideals, establishing both bounds and exact values for special cases.
ER  -