Feynman graphs and hyperplane arrangements defined over F1
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Geometry and Physics"
DOI: 10.1016/j.geomphys.2021.104368
Abstract: Motivated by some computations of Feynman integrals and certain conjectures on mixed Tate motives, Bejleri and Marcolli posed questions about the F1-structure (in the sense of torification) on the complement of a hyperplane arrangement, especially… read more here.
Keywords: space; graphs hyperplane; hyperplane arrangements; feynman graphs ... See more keywords
Lefschetz properties and hyperplane arrangements
Sign Up to like & getrecommendations! Published in 2020 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2020.02.039
Abstract: Abstract In this article, we study the weak and strong Lefschetz properties, and the related notion of almost revlex ideal, in the non-Artinian case, proving that several results known in the Artinian case hold also… read more here.
Keywords: lefschetz properties; hyperplane arrangements; properties hyperplane;
ℤ-local system cohomology of hyperplane arrangements and a Cohen-Dimca-Orlik type theorem
Sign Up to like & getrecommendations! Published in 2022 at "International Journal of Mathematics"
DOI: 10.1142/s0129167x23500441
Abstract: Local system cohomology groups of the complements of hyperplane arrangements have played an important role in the theory of hypergeometric integrals, the topology of Milnor fibers and covering spaces. One of the important theorems is… read more here.
Keywords: local system; cohen dimca; dimca orlik; system cohomology ... See more keywords