Optional project: Using A1-enumerative geometry, or quadratically enriched enumerative geometry, give a Grothendieck--Witt enriched count of the plane conics in P3 meeting 8 general lines or the count of such conics meeting 6 general lines whose planes contain a given general line. Reference Fulton Intersection Theory 3.2.22.
Cameron Darwin, Aygul Galimova, Miao (Pam) Gu, and Stephen McKean Conics Meeting Eight Lines Over Perfect Fields Available on ArXiv 2107.05543