Abstract We prove that the moduli space of rational curves with cyclic action, constructed in our previous work, is realizable as a wonderful compactification complement hyperplane arrangement product projective spaces. By proving general result on such compactifications, we conclude this Chow-equivalent to an explicit toric variety (whose fan can be understood tropical version space), from whi...

We study torsion properties of the twisted Alexander modules affine complement M a complex essential hyperplane arrangement, as well those punctured stratified tubular neighborhoods arrangements. investigate divisibility between polynomials two spaces, compute (first) polynomial neighborhood an line and possible roots both arrangement in higher dimensions. apply our results to distinguish non-h...

Let A be a complex hyperplane arrangement, and let X be a modular element of arbitrary rank in the intersection lattice of A. We show that projection along X restricts to a fiber bundle projection of the complement of A to the complement of the localization AX of A at X. The fiber is the decone of a realization of the complete principal truncation of the underlying matroid of A along the flat c...

We prove an effective version of a theorem of Dufresnoy: For any set of 2n + 1 hyperplanes in general position in Pn, we find an explicit constant K such that for every holomorphic map f from the unit disc to the complement of these hyperplanes, we have f#(0) ≤ K, where f# denotes the norm of the derivative measured with respect to the Fubini-Study metric. This result gives an explicit lower bo...

It is known that the designs PGn−1(n, q) in some cases have spreads of maximal -arcs. Here a -arc is a non-empty subset of points that meets every hyperplane in 0 or points. The situation for designs in general is not so well known. This paper establishes an equivalence between the existence of a spread of -arcs in the complement of a Hadamard design and the existence of an affine design and a ...

Motivated by some computations of Feynman integrals and certain conjectures on mixed Tate motives, Bejleri Marcolli posed questions about the $\mathbb{F}_1$-structure (in sense torification) complement a hyperplane arrangement, especially for an arrangement defined in space cycles graph. In this paper, we prove that has if only it is Boolean. We also cycle graph Boolean basis consisting such an...

The wreath product W (r, n) of the cyclic group of order r and the symmetric group Sn acts on the corresponding projective hyperplane complement, and on its wonderful compactification as defined by De Concini and Procesi. We give a formula for the characters of the representations of W (r, n) on the cohomology groups of this compactification, extending the result of Ginzburg and Kapranov in the...

As is well-known, the homology groups of the complement of a complex hyperplane arrangement are torsion-free. Nevertheless, as we showed in a recent paper [2], the homology groups of the Milnor fiber of such an arrangement can have non-trivial integer torsion. We give here a brief account of the techniques that go into proving this result, outline some of its applications, and indicate some fur...

Abstract. We study the Z2-equivariant K-theory of M(A), where M(A) is the complement of the complexification of a real hyperplane arrangement, and Z2 acts on M(A) by complex conjugation. We compute the rational equivariant Kand KO-rings of M(A), and we give two different combinatorial descriptions of a subring Line(A) of the integral equivariant KO-ring, where Line(A) is defined to be the subri...