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On simplicial arrangements in with splitting polynomial
David Geis
In this paper, we study simplicial hyperplane arrangements in real projective -space. We give a necessary condition for the characteristic polynomial to have only real roots, va…
Combinatorics of free and simplicial line arrangements
David Geis
We study the combinatorics of pseudoline arrangements in the real projective plane. Our focus lies on two classes of arrangements: simplicial arrangements and arrangements whose ch…
Tits arrangements on cubic curves
Michael Cuntz, David Geis
We classify affine rank three Tits arrangements whose roots are contained in the locus of a homogeneous cubic polynomial. We find that there exist irreducible affine Tits arrangeme…
Combinatorial simpliciality of arrangements of hyperplanes
Michael Cuntz, David Geis
We introduce a combinatorial characterization of simpliciality for arrangements of hyperplanes. We then give a sharp upper bound for the number of hyperplanes of such an arrangemen…