论文标题
Cohen-Macaulay本地环，$ e_2 = e_1-e+1 $
Cohen-Macaulay local rings with $e_2 = e_1-e+1$
论文作者
论文摘要
在本文中，我们研究了Cohen -Macaulay尺寸$ D $，Mulutmity $ E $和第二个Hilbert系数$ E_2 $的Cohen -Macaulay $ e_2 = e_2 = e_1-e + 1 $。令$ h =μ（\ mathfrak {m}） - d $。如果$ e_2 \ neq 0 $，则在我们的情况下，我们可以证明该类型$ a \ geq e -h -1 $。如果类型$ a = e -h -1 $，则我们表明相关的级环$ g（a）$是Cohen -Macaulay。在下一个情况下，当类型$ a = e -h $时，我们确定所有可能的希尔伯特系列$ a $。在这种情况下，我们表明Hilbert系列$ a $完全决定了深度$ g（a）$。
In this paper we study Cohen-Macaulay local rings of dimension $d$, multiplicity $e$ and second Hilbert coefficient $e_2$ in the case $e_2 = e_1 - e + 1$. Let $h = μ(\mathfrak{m}) - d$. If $e_2 \neq 0$ then in our case we can prove that type $A \geq e - h -1$. If type $A = e - h -1$ then we show that the associated graded ring $G(A)$ is Cohen-Macaulay. In the next case when type $A = e - h$ we determine all possible Hilbert series of $A$. In this case we show that the Hilbert Series of $A$ completely determines depth $G(A)$.
