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PreprintarXiv licencearXiv

Artin-Schreier geproci configurations in projective spaces of arbitrary dimension

  • Luca Chiantini
  • Lucja Farnik
  • Giuseppe Favacchio
  • Brian Harbourne
  • Juan Migliore
  • Tomasz Szemberg
  • Justyna Szpond
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Abstract

We construct finite geproci sets in every projective dimension and in every positive characteristic by introducing 𝔽N-Artin-Schreier configurations. In ℙ3, we characterize exactly when such configurations are geproci: an 𝔽N-Artin-Schreier configuration on q lines spanning ℙ3 is (q,N)-geproci if and only if q≤ N. We then develop a lifting construction which produces geproci sets in ℙn for every n≥ 3.

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Cite

BibTeXRIS
BibTeX
@misc{chiantini2026artinschreier,
  title = {{Artin-Schreier geproci configurations in projective spaces of arbitrary dimension}},
  author = {Luca Chiantini and Lucja Farnik and Giuseppe Favacchio and Brian Harbourne and Juan Migliore and Tomasz Szemberg and Justyna Szpond},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03024},
  eprint = {2609.03024},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03024},
}
RIS
TY  - UNPB
TI  - Artin-Schreier geproci configurations in projective spaces of arbitrary dimension
AU  - Luca Chiantini
AU  - Lucja Farnik
AU  - Giuseppe Favacchio
AU  - Brian Harbourne
AU  - Juan Migliore
AU  - Tomasz Szemberg
AU  - Justyna Szpond
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.03024
UR  - https://arxiv.org/abs/2609.03024
AB  - We construct finite geproci sets in every projective dimension and in every positive characteristic by introducing 𝔽_N-Artin-Schreier configurations. In ℙ^3, we characterize exactly when such configurations are geproci: an 𝔽_N-Artin-Schreier configuration on q lines spanning ℙ^3 is (q,N)-geproci if and only if q≤ N. We then develop a lifting construction which produces geproci sets in ℙ^n for every n≥ 3.
ER  -