NUMBERS OF Z n - GRADED MODULES
نویسنده
چکیده
Let S = K[X 1 ,. .. , X n ] be the polynomial ring over a field K. For bounded below Z n-graded S-modules M and N we show that if Tor S p (M, N) = 0, then for 0 ≤ i ≤ p, the dimension of the K-vector space Tor S i (M, N) is at least p i. In particular, we get lower bounds for the total Betti numbers. These results are related to a conjecture of Buchsbaum and Eisenbud.
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