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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

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Can view the connected component of the Picard scheme $\text{Pic}^0(X)$ as a "kernel" of the...

So on a curve, $\text{Pic}^0(X)$ is just the Jacobian variety, and just correspond to degree $0$ divisors. One way to extend the notion of divisors corresponding to a vector bundle is taking the first …
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