Heights of hypersurfaces and Igusa's zeta-functions (Q1581871)

The authors associate the height of a hypersurface defined by a polynomial \(P(z)\) to a certain real local zeta function associated to \(\log|P(z)|\). Moreover they give the explicit formulae for some polynomials \(P(z)\). In particular, from their result in the case of \(P(z)= z_0z_1- z_2z_3+ z_4z_5\), they obtain the height of the Grassmann hypersurface \({\mathbf G}(2,4)\).