Generic lines and one fat linear space have good postulation
Let n,d,r∈Nn,d,r\in\mathbb{N}n,d,r∈N with n≥r+2≥3n\geq r+2\geq 3n≥r+2≥3. Let Π≅Pr⊂Pn\Pi\cong\mathbb{P}^r\subset\mathbb{P}^nΠ≅Pr⊂Pn and let X⊂PnX\subset\mathbb{P}^nX⊂Pn consist of s≥1s\geq 1s≥1 generic lines and one mmm-multipl…