Symbolic powers versus regular powers of ideals of general points in P^1XP^1 (versione elettronica pubblicata il 13 Novembre 2012)

Recent work of Ein-Lazarsfeld-Smith and Hochster-Hunekeraised the problem of which symbolic powers of an idealare contained in a given ordinary power of the ideal.Bocci-Harbourne developed methods to address this problem, which involve asymptotic numerical characters ofsymbolic powers of the ideals. Most of the workdone up to now has been done for ideals defining 0-dimensionalsubschemes of projective space.Here we focus on certain subschemes given bya union of lines in $P^3$ which can also be viewedas points in $P^1XP^1$.We also obtain results on theclosely related problem, studied by Hochster and by Li-Swanson, of determining situations for which each symbolic power of an ideal is an ordinary power.