We show that, for every integer $1 \leq d \leq 4$ and every finite set $S$ ofplaces, there exists a degree $d$ del Pezzo surface $X$ over ${\mathbb Q}$ suchthat ${\rm Br}(X)/{\rm Br}({\mathbb Q}) \cong {\mathbb Z}/2{\mathbb Z}$ and theBrauer-Manin obstruction works exactly at the places in $S$. For $d = 4$, weprove that in all cases, with the exception of $S = \{\infty\}$, this surfacemay be chosen diagonalizably over ${\mathbb Q}$.
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机译：我们证明，对于每个整数$ 1 \ leq d \ leq 4 $和每个有限集$ S $ ofplaces，在$ {\ mathbb Q} $上存在一个度数d $ del del Pezzo曲面$ X $，使得$ {\ rm Br}（X）/ {\ rm Br}（{\ mathbb Q}）\ cong {\ mathbb Z} / 2 {\ mathbb Z} $和Brauer-Manin障碍物恰好在$ S $处起作用。对于$ d = 4 $，我们证明在所有情况下，除了$ S = \ {\ infty \} $，可以选择对角线地选择$ {\ mathbb Q} $。
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