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April 2021 Generalized F-signatures of Hibi rings
Akihiro Higashitani, Yusuke Nakajima
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Illinois J. Math. 65(1): 97-120 (April 2021). DOI: 10.1215/00192082-8827655

Abstract

The F-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 focusing on the number of nonfree direct summands. In this paper, we provide several methods to compute the (generalized) F-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) F-signature for some Segre products of polynomial rings.

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Akihiro Higashitani. Yusuke Nakajima. "Generalized F-signatures of Hibi rings." Illinois J. Math. 65 (1) 97 - 120, April 2021. https://doi.org/10.1215/00192082-8827655

Information

Received: 9 December 2019; Revised: 1 September 2020; Published: April 2021
First available in Project Euclid: 16 December 2020

Digital Object Identifier: 10.1215/00192082-8827655

Subjects:
Primary: 13A35
Secondary: 05E40 , 06A11 , 14M25

Rights: Copyright © 2021 by the University of Illinois at Urbana–Champaign

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Vol.65 • No. 1 • April 2021
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