A geometric deletion-restriction formula
Algebraic Geometry
2014-09-22 v1 Combinatorics
Abstract
In this paper, we recover the characteristic polynomial of an arrangement of hyperplanes by computing the rational equivalence class of the variety defined by the logarithmic ideal of the arrangement. The logarithmic ideal was introduced in [arXiv:0907.0896v2] in a study of the critical points of the master function. The above result is used to understand the asymptotic behavior the Hilbert series of the logarithmic ideal. As an application, we prove the Solomon-Terao formula under the tame hypothesis by identifying each side of the formula with a certain specialization of the Hilbert series of the logarithmic ideal.
Cite
@article{arxiv.1110.2799,
title = {A geometric deletion-restriction formula},
author = {Graham Denham and Mehdi Garrousian and Mathias Schulze},
journal= {arXiv preprint arXiv:1110.2799},
year = {2014}
}
Comments
17 pages