Rationality problems of complex algebraic geometry has a long history. Recent developments, usually referred as specialization method in the literature, have given fruitful new examples of non-rational varieties.We give a sufficient condition for a Brauer-Severi surface bundle over a rational 3-fold to not be stably rational. Additionally, we present an example that satisfies this condition and demonstrate the existence of families of Brauer-Severi surface bundles whose general members are smooth and not stably rational.
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