Say I have a variety $X$ over a field $k$ with $\text{Alb}(X)$ trivial, and a fibration in quadrics $f: Y \to X$ (i.e. the fiber above each point of $Y$ is a quadric). Is it true that $\text{Alb}(Y)$ is trivial as well? If so, why?
2026-05-05 02:23:41.1777947821
Triviality of Albanese variety
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