m = 2 case in P5 for 10 ≤ s ≤ 13 general points

Determine whether, for the defining ideal I of s general points in P5 with s ∈ {10, 11, 12, 13}, the inequality â(I) ≥ (a(I(2)) + 4)/6 holds, i.e., whether the m = 2 case of Demailly’s Conjecture is satisfied for these four values of s.

Background

The paper establishes the m = 2 case of Demailly’s Conjecture for very general points in all dimensions and for general points in P3, P4, and P5 except for s = 10, 11, 12, 13 in P5. These four cases remain unresolved and are highlighted explicitly as outstanding.

The authors indicate that improved lower bounds for Waldschmidt constants for 10 points in P5 may resolve these cases, but they are left open.