Generalized F-signatures of Hibi rings
Abstract
The -signature is a numerical invariant defined by the number of free direct summands in the Frobenius push-forward, and it measures singularities in positive characteristic. It can be generalized by focussing on the number of non-free direct summands. In this paper, we provide several methods to compute the (generalized) -signature of a Hibi ring which is a special class of toric rings. In particular, we show that it can be computed by counting the elements in the symmetric group satisfying certain conditions. As an application, we also give the formula of the (generalized) -signature for some Segre products of polynomial rings.
Keywords
Cite
@article{arxiv.1911.08720,
title = {Generalized F-signatures of Hibi rings},
author = {Akihiro Higashitani and Yusuke Nakajima},
journal= {arXiv preprint arXiv:1911.08720},
year = {2020}
}
Comments
16 pages, to appear in Illinois J. Math., v2: minor changes, this is the expanded version of Appendix A of arXiv:1702.07058v1