论文标题
数值半群和多项式身份的属
Genera of numerical semigroups and polynomial identities for degrees of syzygies
论文作者
论文摘要
我们得出了数值半群的任意度$ n $的多项式身份$ n $，s_m = <d_1，...，...，d_m>，并证明n> = m，它们包含较高的g_r = \ sum_ {s _> \ setminus s_m} s_m} s_m的g_r = \ sum_ {我们找到一个数字g_m = b_m-m+1的代数独立属g_r和方程，与g_m+1属相关，其中b_m = \ sum_ {k = 1}^{m-1}^{m-1}β_k，β_k表示非对称半group的总和betti数量。 G_M的数字很大程度上取决于S_M的对称性，并减少对称半群和完整的交集。
We derive polynomial identities of arbitrary degree $n$ for syzygies degrees of numerical semigroups S_m=<d_1,...,d_m> and show that for n>=m they contain higher genera G_r=\sum_{s\in Z_>\setminus S_m}s^r of S_m. We find a number g_m=B_m-m+1 of algebraically independent genera G_r and equations, related any of g_m+1 genera, where B_m=\sum_{k=1}^{m-1}β_k and β_k denote the total and partial Betti numbers of non-symmetric semigroups. The number g_m is strongly dependent on symmetry of S_m and decreases for symmetric semigroups and complete intersections.
