Matroid connectivity and singularities of configuration hypersurfaces
Abstract
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 show that 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.
Keywords
Cite
@article{arxiv.1902.06507,
title = {Matroid connectivity and singularities of configuration hypersurfaces},
author = {Graham Denham and Mathias Schulze and Uli Walther},
journal= {arXiv preprint arXiv:1902.06507},
year = {2021}
}
Comments
64 pages, 4 figures