Minimal graded free resolutions for monomial curves in ?4 defined by almost arithmetic sequences
Minimal graded free resolutions for monomial curves in ?4 defined by almost arithmetic sequences
复制标题
由几乎算术序列定义的 ?4 中单项式曲线的最小分级自由分辨率
DOI：
10.1080/00927872.2016.1175580
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发表时间：
2015
影响因子：
0.7
通讯作者：
Gaurab Tripathi
中科院分区：
文献类型：
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作者：
Achintya Kumar Roy;I. Sengupta;Gaurab Tripathi
设m = (m0, m1, m2, n)是一个几乎等差数列，即gcd(m0, m1, m2, n) = 1的正整数数列，使得m0 < m1 < m2形成一个等差数列，n是任意的，它们最小地生成数值半群Γ =m0 _1 +m1 _1 +m2 _1 +n _1。设k为一个场。参数定义为X0 = tm0, X1 = tm1, X2 = tm2, Y = tn的仿射单项式曲线的齐次坐标环k[Γ]是一个梯度R模，其中R是多项式环k[X0， X1, X2, Y]，其梯度degXi: = mi, degY: = n。本文构造了k[Γ]的最小梯度自由分辨率。
ABSTRACT Let m = (m0, m1, m2, n) be an almost arithmetic sequence, i.e., a sequence of positive integers with gcd(m0, m1, m2, n) = 1, such that m0 < m1 < m2 form an arithmetic progression, n is arbitrary and they minimally generate the numerical semigroup Γ =m0ℕ +m1ℕ +m2ℕ +nℕ. Let k be a field. The homogeneous coordinate ring k[Γ] of the affine monomial curve parametrically defined by X0 = tm0, X1 = tm1, X2 = tm2, Y = tn is a graded R-module, where R is the polynomial ring k[X0, X1, X2, Y] with the grading degXi: = mi, degY: = n. In this paper, we construct a minimal graded free resolution for k[Γ].