Generic Initial Ideals of Arithmetically Cohen–Macaulay Projective Subschemes
Generic Initial Ideals of Arithmetically Cohen–Macaulay Projective Subschemes
复制标题
算术科恩-麦考利射影子方案的一般初始理想
DOI：
10.1080/00927870701329126
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
Jung Pil Park
中科院分区：
文献类型：
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作者：
Hyang Mi Cho;Y. Cho;Jung Pil Park
对于n中的算术Cohen-Macaulay闭子概型X，其饱和定义理想I X k[x 0，...，xn]，设gin（I X）是反字典序下的一般初始理想.本文用特征标fi ′s找到了gin（IX）的生成元的极小系，它将在（3.1）中定义.然后我们得到了deg（X）的特征标公式。对于空间n中的曲线C，我们得到了由一般超平面截面的特征和零星零点个数确定的算术亏格公式。作为应用，我们给出了Ahn和Migliore（2007）和内格尔（1989）中正则性上界的一个新证明：如果X_n是算术Cohen-Macaulay闭子概型，则其中s = {l|（I X）I X 0}。进一步，从IX的一般初始理想的角度给出了算术Cohen-Macaulay闭子概型X的等价条件，表明其上界是尖锐的.
For an arithmetically Cohen–Macaulay closed subscheme X in ℙ n with the saturated defining ideal I X ⊂ k[x 0,…, x n ], let gin(I X ) be the generic initial ideal under the reverse lexicographic order. In this article, we find the minimal system of generators of gin (I X ) in terms of characters f i ′s, which will be defined in (3.1). Then we obtain the formula for deg(X) in terms of characters. For a curve C in ℙ n , we get the formula for the arithmetic genus in terms of characters of a general hyperplane section and the number of sporadic zeros. As an application, we give a new proof of the following upper bound on the regularity given in Ahn and Migliore (2007) and Nagel (1989): if X ⊂ ℙ n is an arithmetically Cohen–Macaulay closed subscheme, then where s = {l | (I X ) l ≠ 0}. Furthermore we give an equivalent condition for an arithmetically Cohen–Macaulay closed subscheme X ⊂ ℙ n to satisfy the equality from the view point of the generic initial ideal of I X , this shows that the upper bound is sharp.
DOI：
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发表时间：
2006
期刊：
Integrable systems, geometry, and topology, AMS/IP Studies of Advanced Mathematics, American Mathematical Society 36
影响因子：
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作者：
FURUYA;Jun;Martin Guest
通讯作者：
Martin Guest