Initial ideals, Veronese subrings, and rates of algebras

Details Initial ideals, Veronese subrings, and rates of algebras Initial ideals, Veronese subrings, and rates of algebras

1993-10-11

arxiv.org/abs/alg-geom/9310007v1

Mathematics

Commutative Algebra

24 pages, latex file

Scientific paper

We show that high Veronese subrings of any commutative graded ring have a Grobner basis with all relations of degree 2. (The d-th Veronese subring of a ring A_0 + A_1 + A_2 + ... is the ring A_0 + A_d + A_{2d} + ...; ``high'' means we take d sufficiently large, say at least half the regularity of the ideal defining the original ring.) This gives another proof of Backelin's theorem that such Veronese subrings are Koszul algebras (= wonderful rings), i.e., that the minimal resolution of the residue field of such a ring is linear.

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