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The Orlik--Solomon algebra of a locally geometric poset and cohomology of complex abelian arrangements — arXiv:2608.23384

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.23384
License (as archived): CC0-1.0
Archived: 2026-10-18T08:33:34.939Z
SHA-256 of the archived text: 4af7ea11e4ca66b89bd4e6b994ec22b58b8fecb701fd05f4d5fa35b732b70eb1
Stable URL of this page: https://metraipolis.com/documento/dc_86c883efd71d

How to cite

The Orlik--Solomon algebra of a locally geometric poset and cohomology of complex abelian arrangements — arXiv:2608.23384 — arXiv (en), https://arxiv.org/abs/2608.23384 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_86c883efd71d (Metraipolis archive dc_86c883efd71d, sha256 4af7ea11e4ca66b89bd4e6b994ec22b58b8fecb701fd05f4d5fa35b732b70eb1)

BibTeX

@misc{dc86c883efd71d,
  title = {The Orlik--Solomon algebra of a locally geometric poset and cohomology of complex abelian arrangements — arXiv:2608.23384},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.23384},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_86c883efd71d; sha256 4af7ea11e4ca66b89bd4e6b994ec22b58b8fecb701fd05f4d5fa35b732b70eb1},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.23384. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

We construct an Orlik--Solomon algebra for any locally geometric poset as a natural generalization of the one for geometric lattices. This algebra has several interesting features, including a combinatorial no-broken-circuit basis that we obtain through Gröbner basis theory. When the poset captures the intersection data of an arrangement of certain subgroups in a complex abelian Lie group, we infuse the Orlik--Solomon algebra with topological information to compute the cohomology of the arrangement complement. In particular, when the Lie group is compact, we present an explicit differential graded algebra whose cohomology is the rational cohomology of the arrangement complement. We further exhibit a family of abelian arrangements whose integer cohomology has torsion.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-25 in math.CO).
Categorie arXiv: Combinatorics (math.CO) ; Algebraic Topology (math.AT).
Pagina del lavoro: https://arxiv.org/abs/2608.23384 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-18T08:27:54.459Z dalla pagina https://arxiv.org/catchup/math.CO/2026-08-25?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).