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A continuously varying family of one-dimensional vector spaces over a topological space. A related tag is the vector-bundles tag.

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Square root of the determinant line

There is no such isomorphism (at least for $g \geq 9$). In O. Randal-Williams, The Picard group of the moduli space of r-Spin Riemann surfaces. Advances in Mathematics 231 (1) (2012) 482-515. I co …
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