Letρ _C be the regularity of the Hilbert function of a projective curveC inP ⁿ _K over an algebraically closed fieldK andβ ₁,...,β _n-1 be degrees for which there exists a complete intersection of type (β ₁,...,β _n-1) containing properlyC. Then the Castelnuovo-Mumford regularity ofC is bounded above by max {ρ _C + 1,β ₁ +...+β _n-1-(n-1)}. We investigate the sharpness of the above bound, which is achieved by curves algebraically linked to ones having degenerate general hyperplane section.

中文翻译：

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最小生成器和希尔伯特函数的规则性边界

让ρ _Ç是投影曲线的希尔伯特功能的规律性Ç在P ^Ñ _ķ通过一个代数闭域ķ和β ₁，...，β _{Ñ -1}是存在用于其类型的一个完整的相交度（β ₁，...，β _{ñ -1}）含有正确ç。然后的卡斯德尔诺-芒福德规律性Ç上面由最大边界{ ρ _{c ^} + 1，β ₁ + ... + β _{Ñ -1} - （Ñ -1）}。我们研究了上述边界的清晰度，这是通过代数链接到具有退化的一般超平面截面的曲线来实现的。