Hilbert Functions of Veronese Algebras
نویسندگان
چکیده
We study the Hilbert polynomials of non-standard graded algebras R, that are finitely generated on generators not all of degree one. Given an expression P (R, t) = a(t)/(1 − t) for the Poincaré series of R as a rational function, we study for 0 ≤ i ≤ l the graded subspaces ⊕kRkl+i (which we denote R[l; i]) of R, in particular their Poincaré series and Hilbert functions. For example, we prove that if R[l; i] 6= 0 then its Hilbert polynomial has degree n− 1. We investigate the algebraic invariants of finite groups in this context.
منابع مشابه
The Hilbert Series of Algebras of Veronese Type
This paper gives an explicit formula for the Hilbert series of algebras of Veronese type.
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