Given a Fourier-Mukai transform $\Phi$ between the bounded derived categories of two smooth projective curves, we verifiy that the induced map between the Jacobian varieties preserves the principal polarization if and only if $\Phi$ is an equivalence.
The rank-one limit of the Fourier-Mukai transform
GV-sheaves, Fourier-Mukai transform, and Generic Vanishing
M-regularity and the Fourier-Mukai transform
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