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Let $S=k[X_1,\cdots,X_n]$ and $\{f_1,\cdots f_q\}$ be a $S$-regular sequence with ${\rm deg}(f_i)=a_i$.

What is Hilbert polynomial of $S/ \langle f_1,\cdots,f_q\rangle$?

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    Hint: The Koszul complex of a regular sequence is exact.2012-09-04
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    Thanks David, but I know it, I can't easily formulate it's Hilbert polynomial.2012-09-04
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    Hint 2: Can you compute the Hilbert polynomials of the other terms in the Koszul complex?2012-09-04
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    sorry, david, I don't understand your hint. maybe induction on q?2012-09-05
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    That can be made to work as well. Can you do $q=1$? Can you do $q=2$? If you can do $q=2$, I think you should be able to see the rest.2012-09-05
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    I See $q=1$ case. but In case $q=2$, I can't calculate combinations.2012-09-06

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