The F-pure threshold of quasi-homogeneous polynomials

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Inspired by the work of Bhatt and Singh (see: arXiv:1307.1171) we compute the F-pure threshold of quasi-homogeneous polynomials. We first consider the case of a curve given by a quasi-homogeneous polynomial f in three variables x,y,z of degree equal to the degree of xyz and then we proceed with the general case of a Calabi-Yau hypersurface, i.e. a hypersurface given by a quasi-homogeneous polynomial f in n+1 variables x₀,, xₙ of degree equal to the degree of x₀ xₙ.