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# Initial ideals , Veronese subrings , and rates of algebras ( To appear in Advances in Mathematics )

@inproceedings{Eisenbud1994InitialI, title={Initial ideals , Veronese subrings , and rates of algebras ( To appear in Advances in Mathematics )}, author={David Eisenbud}, year={1994} }

- Published 1994

Let S be a polynomial ring over an infinite field and let I be a homogeneous ideal of S. Let T d be a polynomial ring whose variables correspond to the monomials of degree d in S. We study the initial ideals of the ideals V d (I) ⊂ T d that define the Veronese subrings of S/I. In suitable orders, they are easily deduced from the initial ideal of I. We show that in(V d (I)) is generated in degree ≤ max(⌈reg(I)/d⌉, 2), where reg(I) is the regularity of the ideal I. (In other words, the d th… CONTINUE READING