# On parametrizing exceptional tangent cones to Prym theta divisors

@article{Smith2016OnPE, title={On parametrizing exceptional tangent cones to Prym theta divisors}, author={Roy Smith and Robert Varley}, journal={Transactions of the American Mathematical Society}, year={2016}, volume={369}, pages={3763-3798} }

The theta divisor of a Jacobian variety is parametrized by a smooth divisor variety via the Abel map, with smooth projective linear fibers. Hence the tangent cone to a Jacobian theta divisor at any singularity is parametrized by an irreducible projective linear family of linear spaces normal to the corresponding fiber. The divisor variety X parametrizing a Prym theta divisor Ξ on the other hand, is singular over any exceptional point, hence although the fibers of the Abel Prym map are still…

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