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PreprintCC BY 4.0arXiv

The Non-Lefschetz Locus of Monomial Complete Intersections in Positive Characteristic

  • Adam LaClair
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Abstract

In the 1980s, Stanley and J. Watanabe proved that over a field of characteristic zero every monomial complete intersection has the strong Lefschetz property. Determining which monomial complete intersections in positive characteristic have the weak Lefschetz property has been the subject of ongoing research. In this paper, we give a complete description of the locus of exponent vectors corresponding to monomial complete intersections over a field of positive characteristic that fail the weak Lefschetz property. We describe this locus explicitly in terms of translates of positive-orthant lattice balls in the taxicab metric.

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Cite

BibTeXRIS
BibTeX
@misc{laclair2026nonlefschetz,
  title = {{The Non-Lefschetz Locus of Monomial Complete Intersections in Positive Characteristic}},
  author = {Adam LaClair},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26738},
  eprint = {2609.26738},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26738},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Non-Lefschetz Locus of Monomial Complete Intersections in Positive Characteristic
AU  - Adam LaClair
PY  - 2026
DA  - 2026/09/30
PB  - arXiv
DO  - 10.48550/arxiv.2609.26738
UR  - https://arxiv.org/abs/2609.26738
AB  - In the 1980s, Stanley and J. Watanabe proved that over a field of characteristic zero every monomial complete intersection has the strong Lefschetz property. Determining which monomial complete intersections in positive characteristic have the weak Lefschetz property has been the subject of ongoing research. In this paper, we give a complete description of the locus of exponent vectors corresponding to monomial complete intersections over a field of positive characteristic that fail the weak Lefschetz property. We describe this locus explicitly in terms of translates of positive-orthant lattice balls in the taxicab metric.
ER  -