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Let $F$ be the Macaulay dual generator for $\\mathcal{A}$. We compute explicitly the Hessian determinant $|\\frac{\\partial ^2F}{\\partial X_i \\partial X_j}|$ evaluated at the point $X_1 = X_2 = \\cdots = X_N=1$ and relate it to the determinant of the incidence matrix between $\\mathcal{V}_1$ and $\\mathcal{V}_{n-1}$. 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Let $F$ be the Macaulay dual generator for $\\mathcal{A}$. We compute explicitly the Hessian determinant $|\\frac{\\partial ^2F}{\\partial X_i \\partial X_j}|$ evaluated at the point $X_1 = X_2 = \\cdots = X_N=1$ and relate it to the determinant of the incidence matrix between $\\mathcal{V}_1$ and $\\mathcal{V}_{n-1}$. 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