Homotopy type of Frobenius complexes
Commutative Algebra
2013-08-15 v1 Algebraic Topology
Abstract
A submonoid A of N^d has a natural order defined by a <= a + b for elements a and b of A. The Frobenius complex is the order complex of an open interval of A with respect to this order. In this paper, the homotopy type of the Frobenius complex of A is determined when A is the submonoid of N generated by two relatively prime integers, or the submonoid of N^2 generated by three elements of which any two are linearly independent. As an application, the multigraded Poincare series of the quotient algebra K[x, y, z] / (x^p y^q - z^r) over a field K is determined and proved to be rational.
Keywords
Cite
@article{arxiv.1308.2805,
title = {Homotopy type of Frobenius complexes},
author = {Shouta Tounai},
journal= {arXiv preprint arXiv:1308.2805},
year = {2013}
}