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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

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
Full Text: DOI
[1] DOI: 10.1016/0021-8693(86)90076-1 · Zbl 0588.13013
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[4] DOI: 10.1016/0022-4049(86)90029-0 · Zbl 0586.13015
[5] DOI: 10.2307/2373744 · Zbl 0244.13012
[6] DOI: 10.1090/S0002-9947-1984-0748843-4
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