1
$\begingroup$

For a graded finitely generated $k[x_1, \cdots, x_n]$ module $V$, I know that $ b_{i,p}(V)=\operatorname{dim}_k H_i(K\otimes V)_p$ where $K$ be the Koszul complex of $k$.

I also know that $K$ is minimal. then is always $H_i(K\otimes V)=0$ for $i=1,\cdots n-1$?

  • 0
    sorry Matt. question error. you corrent. $H_0(K\otimes V)$ be nonzero.2012-08-06

0 Answers 0