POSTULATION OF FINITE SETS IN P 3 WITH h 1 (IS(m)) > 0 AND ♯(S) 4m
Edoardo Ballico · 2012
Fix an integer m ≥ 23. Here we give the list of all finite sets S ⊂ P 3 such that ♯(S) ≤ 4m and h 1 (IS(m)) > 0. Fix an integer ǫ ≥ 0. We prove that if m ≫ ǫ, then there is no finite set A ⊂ P 3 such that ♯(A) ≤ 4m+ǫ, h 0 (IA(2)) = 0, h 1 (IA(m)) > 0 and h 1 (IA '(m)) = 0 for any A ' ( A.