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Winter 2020 $F$-pure threshold and height of quasihomogeneous polynomials
Susanne Müller
J. Commut. Algebra 12(4): 559-572 (Winter 2020). DOI: 10.1216/jca.2020.12.559

Abstract

The aim of this paper is to give a connection between the F-pure threshold of a polynomial and the height of the corresponding Artin–Mazur formal group. For this, we consider a quasihomogeneous polynomial f[x0,,xN] of degree w equal to the degree of x0xN and show that the F-pure threshold of the reduction fp𝔽p[x0,,xN] is equal to the log-canonical threshold of f if and only if the height of the Artin–Mazur formal group associated to HN1(X,𝔾m,X), where X is the hypersurface given by f, is equal to 1. We also prove that a similar result holds for Fermat hypersurfaces of degree greater than N+1. Furthermore, we give examples of weighted Delsarte surfaces which show that other values of the F-pure threshold of a quasihomogeneous polynomial of degree w cannot be characterized by the height.

Citation

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Susanne Müller. "$F$-pure threshold and height of quasihomogeneous polynomials." J. Commut. Algebra 12 (4) 559 - 572, Winter 2020. https://doi.org/10.1216/jca.2020.12.559

Information

Received: 7 June 2017; Revised: 7 December 2017; Accepted: 2 February 2018; Published: Winter 2020
First available in Project Euclid: 5 January 2021

MathSciNet: MR4194941
Digital Object Identifier: 10.1216/jca.2020.12.559

Subjects:
Primary: 13A35, 14B05, 32S35

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.12 • No. 4 • Winter 2020
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