Blowing up a non-split Severi–Brauer surface at reduced points is del Pezzo exactly for one degree-3/6 point or two degree-3 points in the stated non-nodal condition.
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General position on Severi--Brauer surfaces
Blowing up a non-split Severi–Brauer surface at reduced points is del Pezzo exactly for one degree-3/6 point or two degree-3 points in the stated non-nodal condition.