In this paper, we investigate certain graded-commutative rings which are related to the reciprocal plane compactification of coordinate ring a complement hyperplane arrangement. We give presentation these by generators and defining relations. This was used Holler I. Kriz calculate $\mathbb{Z}$-graded coefficients localizations ordinary $RO((\mathbb{Z}/p)^n)$-graded equivariant cohomology at giv...

sueyoshi and sekitani in 2007 presented a paper that explores the measurement of returns to scale under a possible occurrence of multiple solution in a reference set and a supporting hyperplane. the occurrence ofmultiple solutions is classified into type i and type ii. type i is an occurrence of multiple solutions in a reference set. type ii is an occurrence of multiple solutions on a supportin...

We construct a new class of maximal acyclic matchings on the Salvetti complex locally finite hyperplane arrangement. Using discrete Morse theory, we then obtain an explicit proof minimality complement. Our construction provides interesting insights also in well-studied case arrangements, and gives nice geometric description Betti numbers In particular, solve conjecture Drton Klivans characteris...

The study of the topology of hypersurface complements is a classical subject in algebraic geometry. Most of what is known about these spaces is related to invariants of their rational homotopy type. In this paper, we attempt to show that their Fp-homotopy type captures in general more information than the Q-homotopy type, where Fp is the prime field of p elements. Let X be the complement to a h...

If X is the complement of a hypersurface in P, then Kohno showed in [9] that the nilpotent completion of π1(X) is isomorphic to the nilpotent completion of the holonomy Lie algebra of X. When X is the complement of a hyperplane arrangement A, the ranks φk of the lower central series quotients of π1(X) are known in only two very special cases: if X is hypersolvable (in which case the quadratic c...

Let V be a degree d, reduced hypersurface in CP, n ≥ 1, and fix a generic hyperplane, H. Denote by U the (affine) hypersurface complement, CP−V ∪H, and let U be the infinite cyclic covering of U corresponding to the kernel of the linking number homomorphism. Using intersection homology theory, we give a new construction of the Alexander modules Hi(U ;Q) of the hypersurface complement and show t...

We use stratified Morse theory to construct a complex to compute the cohomology of the complement of a hyperplane arrangement with coefficients in a complex rank one local system. The linearization of this complex is shown to be the Aomoto complex of the arrangement. Using this result, we establish the relationship between the cohomology support loci of the complement and the resonance varietie...

The stratum $$\mathcal {H}(a,-b_{1},\dots ,-b_{p})$$ of meromorphic 1-forms with a zero order and poles orders $$b_{1},\dots ,b_{p}$$ on the Riemann sphere has map, isoresidual fibration, defined by assigning to any differential its residues at poles. We show that above complement hyperplane arrangement, resonance fibration is an unramified cover degree $$\frac{a!}{(a+2-p)!}$$ . Moreover, monod...