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Article: Total positivity for matroid Schubert varieties
| Title | Total positivity for matroid Schubert varieties |
|---|---|
| Authors | |
| Issue Date | 1-Sep-2025 |
| Publisher | Springer |
| Citation | Selecta Mathematica (New Series), 2025, v. 31 How to Cite? |
| Abstract | We define the totally nonnegative matroid Schubert variety $\mathcal Y_V$ of a linear subspace $V\subset\mathbb R^n$. We show that $\mathcal Y_V$ is a regular CW complex homeomorphic to a closed ball, with strata indexed by pairs of acyclic flats of the oriented matroid of $V$. This closely resembles the regularity theorem for totally nonnegative generalized flag varieties. As a corollary, we obtain a regular CW structure on the real matroid Schubert variety of $V$. |
| Persistent Identifier | http://hdl.handle.net/10722/359419 |
| ISSN | 2023 Impact Factor: 1.2 2023 SCImago Journal Rankings: 1.715 |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | He, Xuhua | - |
| dc.contributor.author | Simpson, Connor | - |
| dc.contributor.author | Xie, Kaitao | - |
| dc.date.accessioned | 2025-09-03T00:30:24Z | - |
| dc.date.available | 2025-09-03T00:30:24Z | - |
| dc.date.issued | 2025-09-01 | - |
| dc.identifier.citation | Selecta Mathematica (New Series), 2025, v. 31 | - |
| dc.identifier.issn | 1022-1824 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/359419 | - |
| dc.description.abstract | <p>We define the totally nonnegative matroid Schubert variety $\mathcal Y_V$ of a linear subspace $V\subset\mathbb R^n$. We show that $\mathcal Y_V$ is a regular CW complex homeomorphic to a closed ball, with strata indexed by pairs of acyclic flats of the oriented matroid of $V$. This closely resembles the regularity theorem for totally nonnegative generalized flag varieties. As a corollary, we obtain a regular CW structure on the real matroid Schubert variety of $V$.<br></p> | - |
| dc.language | eng | - |
| dc.publisher | Springer | - |
| dc.relation.ispartof | Selecta Mathematica (New Series) | - |
| dc.rights | This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. | - |
| dc.title | Total positivity for matroid Schubert varieties | - |
| dc.type | Article | - |
| dc.description.nature | published_or_final_version | - |
| dc.identifier.doi | 10.1007/s00029-025-01080-3 | - |
| dc.identifier.volume | 31 | - |
| dc.identifier.eissn | 1420-9020 | - |
| dc.identifier.issnl | 1022-1824 | - |