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We derive polynomial identities of arbitrary degree $n$ for syzygies degreesof numerical semigroups S_m=<d_1,...,d_m> and show that for n>=m they containhigher genera G_r=\sum_{s\in Z_>\setminus S_m}s^r of S_m. We find a numberg_m=B_m-m+1 of algebraically independent genera G_r and equations, related anyof g_m+1 genera, where B_m=\sum_{k=1}^{m-1}\beta_k and \beta_k denote the totaland partial Betti numbers of non-symmetric semigroups. The number g_m isstrongly dependent on symmetry of S_m and decreases for symmetric semigroupsand complete intersections.

Genera of numerical semigroups and polynomial identities for degrees of syzygies