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math.CO2025
Reconstruction of oriented matroids from Varchenko-Gelfand algebras
Yukino Yagi, Masahiko Yoshinaga
The algebra of -valued functions on the set of chambers of a real hyperplane arrangement is called the Varchenko-Gelfand (VG) algebra. This algebra carries a natural filtration…
math.AG2025
Milnor fibrations and oriented matroids
Paul Mücksch, Masahiko Yoshinaga
We introduce a combinatorial model for the Milnor fibration of a complexified real arrangement using oriented matroids. It is a poset quasi-fibration, whose domain is a subdivision…
math.AG2025
Maximal Betti number for local system cohomology of hyperplane arrangement complements
Yongqiang Liu, Masahiko Yoshinaga
Let be a rank one local system with field coefficient on the complement of an essential complex hyperplane arrangement in $\mathbb{C}^\…