Asymptotic linearity of regularity and a*-invariant of powers of ideals

Details Asymptotic linearity of regularity and a*-invariant of powers of ideals Asymptotic linearity of regularity and a*-invariant of powers of ideals

2009-11-30

arxiv.org/abs/0911.5537v2

Mathematics

Commutative Algebra

11 pages, revision: get rid of the condition that R is a polynomial ring in the last theorem.

Scientific paper

Let X = Proj R be a projective scheme over a field k, and let I be an ideal in R generated by forms of the same degree d. Let Y --> X be the blowing up of X along the subscheme defined by I, and let f: Y --> Z be the projection of Y given by the divisor dH - E, where E is the exceptional divisor of the blowup and H is the pullback of a general hyperplane in X. We investigate how the asymptotic linearity of the regularity and a*-invariant of I^q (for q large) is related to invariants of fibers of f.

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