Matroid connectivity and singularities of configuration hypersurfaces
- Consider a linear realization of a matroid over a field. One associates with it a configuration polynomial and a symmetric bilinear form with linear homogeneous coefficients. The corresponding configuration hypersurface and its non-smooth locus support the respective first and second degeneracy scheme of the bilinear form.We showthat these schemes are reduced and describe the effect of matroid connectivity: for (2-)connected matroids, the configuration hypersurface is integral, and the second degeneracy scheme is reduced Cohen–Macaulay of codimension 3. If the matroid is 3-connected, then also the second degeneracy scheme is integral. In the process, we describe the behavior of configuration polynomials, forms and schemes with respect to various matroid constructions.
Author: | Graham Denham, Mathias SchulzeORCiD, Uli Walther |
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URN: | urn:nbn:de:hbz:386-kluedo-78423 |
DOI: | https://doi.org/10.1007/s11005-020-01352-3 |
ISSN: | 1573-0530 |
Parent Title (English): | Letters in Mathematical Physics |
Publisher: | Springer Nature - Springer |
Document Type: | Article |
Language of publication: | English |
Date of Publication (online): | 2024/03/18 |
Year of first Publication: | 2021 |
Publishing Institution: | Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau |
Date of the Publication (Server): | 2024/03/18 |
Issue: | 111 |
Article Number: | 11 |
Page Number: | 67 |
Source: | https://link.springer.com/article/10.1007/s11005-020-01352-3 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Mathematik |
DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 510 Mathematik |
Collections: | Open-Access-Publikationsfonds |
Licence (German): | Zweitveröffentlichung |