3 research outputs found
Deletion-restriction in toric arrangements
Deletion-restriction is a fundamental tool in the theory of hyperplane
arrangements. Various important results in this field have been proved using
deletion-restriction. In this paper we use deletion-restriction to identify a
class of toric arrangements for which the cohomology algebra of the complement
is generated in degree . We also show that for these arrangements the
complement is formal in the sense of Sullivan.Comment: v2: typos fixed, 11 pages. Accepted for publication in Journal of
Ramanujan Mathematical Societ
Orbit closures of representations of source-sink Dynkin quivers
We use the geometric technique, developed by Weyman, to calculate the
resolution of orbit closures of representations of Dynkin quivers with every
vertex being source or sink. We use this resolution to derive the normality of
such orbit closures. As a consequence we obtain the normality of certain orbit
closures of type E.Comment: 11 pages, 3 figure
Face counting formula for toric arrangements defined by root systems
A toric arrangement is a finite collection of codimension-1 subtori in a torus. The intersections of these subtori stratify the ambient torus into faces of various dimensions. The incidence relations among these faces give rise to many interesting combinatorial problems. One such problem is to obtain a closed-form formula for the number of faces in terms of the intrinsic arrangement data. In this paper we focus on toric arrangements defined by crystallographic root systems. Such an arrangement is equipped with an action of the associated Weyl group. The main result is a formula that expresses the face numbers in terms of a sum of indices of certain subgroups of this Weyl group. Keywords: Toric arrangements, Face enumerations, f-vector, Affine Weyl group