We relate properties of linear systems on X to the question of when I^r contains I^(m) in the case that I is the homogeneous ideal of a finite set of distinct points p_1,...,p_n in P^2, where X is the surface obtained by blowing up the points. We obtain complete answers for when I^r contains I^(m) when the points p_i's lie on a smooth conic or when the points are general and n ≤ 9.
Bocci, C., Harbourne, B. (2010). The resurgence of ideals of points and the containment problem. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 138(4), 1175-1190 [10.1090/S0002-9939-09-10108-9].
The resurgence of ideals of points and the containment problem
BOCCI, CRISTIANO;
2010-01-01
Abstract
We relate properties of linear systems on X to the question of when I^r contains I^(m) in the case that I is the homogeneous ideal of a finite set of distinct points p_1,...,p_n in P^2, where X is the surface obtained by blowing up the points. We obtain complete answers for when I^r contains I^(m) when the points p_i's lie on a smooth conic or when the points are general and n ≤ 9.
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https://hdl.handle.net/11365/21284
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