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