科研之友
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摘要
Let K be an infinite field and let m(1) < < m(n) be a generalized arithmetic sequence of positive integers, i.e., there exist h,d,m(1) epsilon Z(+) such that m(i)=hm(1)+(i-1)d for all i epsilon{2,n}. We consider the projective monomial curve C subset of P-K(n) parametrically defined by x(1)=s(m1)t(mn-m1),...,x(n-1) =s(mn-1)t(mn-mn-1),x(n)=s(mn),x(n+1)=t(mn). In this work, we characterize the Cohen-Macaulay and Koszul properties of the homogeneous coordinate ring K[C] of C. Whenever K[C] is Cohen-Macaulay we also obtain a formula for its Cohen-Macaulay type. Moreover, when h divides d, we obtain a minimal Grobner basis G of the vanishing ideal of C with respect to the degree reverse lexicographic order. From G we derive formulas for the Castelnuovo-Mumford regularity, the Hilbert series and the Hilbert function of K[C] in terms of the sequence.
- 出版日期2017-8
