Non-level semi-standard graded Cohen-Macaulay domain with h-vector (h(0), h(1), h(2))

作者：Higashitani Akihiro; Yanagawa Kohji^*

来源：Journal of Pure and Applied Algebra, 2018, 222(1): 191-201.

DOI：10.1016/j.jpaa.2017.03.011

Let k be an algebraically closed field of characteristic 0, and A = circle plus(i is an element of N) A(i) Cohen-Macaulay graded domain with A(0) = k. If A is semi-standard graded (i.e., A is finitely generated as a k[A(1)]-module), it has the h-vector (h(0), h(1),...,h(s)), which encodes the Hilbert function of A. From now on, assume that s = 2. It is known that if A is standard graded (i.e., A = k[A1]), then A is level. We will show that, in the semi-standard case, if A is not level, then h1 + 1 divides h2. Conversely, for any positive integers h and n, there is a non-level A with the h-vector (1, h, (h + 1)n). Moreover, such examples can be constructed as Ehrhart rings (equivalently, normal toric rings).

• 出版日期2018-1