Comparing Powers and Symbolic Powers of Ideals
نویسنده
چکیده
We develop tools to study the problem of containment of symbolic powers I(m) in powers I for a homogeneous ideal I in a polynomial ring k[P ] in N + 1 variables over an arbitrary algebraically closed field k. We obtain results on the structure of the set of pairs (r, m) such that I(m) ⊆ I. As corollaries, we show that I2 contains I(3) whenever S is a finite generic set of points in P2 (thereby giving a partial answer to a question of Huneke), and we show that the containment theorems of [ELS] and [HH1] are optimal for every fixed dimension and codimension.
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