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

2009/11/30 by Huy Tai Ha, Ha, Huy Tai
Mathematics · #13D02 #13D45 #14B15 #14F05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13D02 #msc:13D45 #msc:14B15 #msc:14F05

paper · pdf · doi:10.48550/arxiv.0911.5537

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

arxiv created 2010/04/06 · arxiv updated 2010/04/08

Abstract

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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