Fat lines in P^3: powers versus symbolic powers

摘要

We study the symbolic and regular powers of ideals I for a family of specialconfigurations of lines in P^3. For this family, we show that I^(m) = I^m forall integers m if and only if I^(3) = I^3. We use these configurations toanswer a question of Huneke that asks whether I^(m) = I^m for all m if equalityholds when m equals the big height of the ideal I.