Non-level semi-standard graded Cohen–Macaulay domain with h-vector (h0,h1,h2) |
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Authors: | Akihiro Higashitani Kohji Yanagawa |
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Institution: | 1. Department of Mathematics, Kyoto Sangyo University, Motoyama, Kamigamo, Kita-Ku, Kyoto, 603-8555, Japan;2. Department of Mathematics, Kansai University, Suita, Osaka 564-8680, Japan |
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Abstract: | Let be an algebraically closed field of characteristic 0, and a Cohen–Macaulay graded domain with . If A is semi-standard graded (i.e., A is finitely generated as a -module), it has the h-vector, which encodes the Hilbert function of A. From now on, assume that . It is known that if A is standard graded (i.e., ), then A is level. We will show that, in the semi-standard case, if A is not level, then divides . Conversely, for any positive integers h and n, there is a non-level A with the h-vector . Moreover, such examples can be constructed as Ehrhart rings (equivalently, normal toric rings). |
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