The F-pure threshold of quasi-homogeneous polynomials

Inspired by the work of Bhatt and Singh 3] 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 $x_0,\dots ,x_n$ of degree equal to the degree of $x_0?x_n$.