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PreprintarXiv licencearXiv

Duals of algebraic matroids need not be algebraic

  • Matt Larson
  • Tuong Le
Open at sourcePDFDOICite

Abstract

We give an example showing that the dual of an algebraic matroid need not be algebraic. Our example is a matroid of rank 6 on 10 elements which is algebraic in characteristic 2. It is obtained by gluing an algebraic realization of the non-Fano matroid to a realization of the Fano matroid. Its dual is shown not to be algebraic using the Ingleton-Main lemma.

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Cite

BibTeXRIS
BibTeX
@misc{larson2026duals,
  title = {{Duals of algebraic matroids need not be algebraic}},
  author = {Matt Larson and Tuong Le},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02834},
  eprint = {2609.02834},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02834},
}
RIS
TY  - UNPB
TI  - Duals of algebraic matroids need not be algebraic
AU  - Matt Larson
AU  - Tuong Le
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.02834
UR  - https://arxiv.org/abs/2609.02834
AB  - We give an example showing that the dual of an algebraic matroid need not be algebraic. Our example is a matroid of rank 6 on 10 elements which is algebraic in characteristic 2. It is obtained by gluing an algebraic realization of the non-Fano matroid to a realization of the Fano matroid. Its dual is shown not to be algebraic using the Ingleton-Main lemma.
ER  -