English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A matroid is a machine capturing linearity of mathematical objects andproducing combinatorial structures. Matroid structure arises everywhere sincelinearity is a ubiquitous concept. One natural way to obtain matroids is byconsidering hyperplane arrangements, which give rise to convex polytopes calledmatroid polytopes. Much research has been conducted on these three areas:matroids, matroid polytopes, and hyperplane arrangements. However, substantialgaps in our knowledge remain, and the correspondence diagram between thoseareas needs to be more extensive. For instance, currently, there is no matroidcounterpart of a matroid subdivision, and only some matroid subdivisions areassociated with stable hyperplane arrangements. Moreover, we need a deeperunderstanding of the face structure of a matroid polytope and how to glue orsubdivide base polytopes; the latter requires overcoming Mnev's universalitytheorem. Another interesting question is whether the birational geometry ofhyperplane arrangements can be implemented over matroids. In this paper, wedevelop a theory that integrates the three areas into a trinity relationshipand provide solutions to the aforementioned questions while answering as manyas possible.

Birational Geometry of Matroids and Abstract Hyperplane Arrangements