$X$ is an algebraic surface (i.e. compact complex, which embeds in a projective space). $V$ is a vector bundle of rank 2 over $X$. Why is $\det{V}=\mathcal{O}_X(D)$ for some divisor $D$? Is there a general statement? Thank you.
2026-04-02 08:14:12.1775117652
Quick question: Determinant bundle is Cartier?
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