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The linear syzygies of generic forms. (English) Zbl 0619.13007
Let $$F_ 1,...,F_ n$$ be ”generic” forms of degrees $$d_ i$$ in the polynomial ring $$R=k[x_ 1,...,x_ r]$$ over an infinite field k. Let $$Q=R/(F_ 1,...,F_ n)$$. Let d be the least degree of the forms. Then, in the Hilbert series, $$Hilb_ Q(Z)=\sum^{\infty}_{j=0}\dim_ kQ_ jZ^ j,\quad \dim_ kQ_{d+1}=\max \{0,N(r,d+1)-rn\}$$, where $$N(r,d+1)=\dim_ kR_{d+1}=\left( \begin{matrix} d+r\\ d+1\end{matrix} \right)$$.
Reviewer: R.M.Najar

MSC:
 13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.) 13F20 Polynomial rings and ideals; rings of integer-valued polynomials
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References:
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