# Severi varieties on blow--ups of the symmetric square of an elliptic curve

@inproceedings{Ciliberto2021SeveriVO, title={Severi varieties on blow--ups of the symmetric square of an elliptic curve}, author={Ciro Ciliberto and Thomas Dedieu and Concettina Galati and Andreas Leopold Knutsen}, year={2021} }

We prove that certain Severi varieties of nodal curves of positive genus on general blow–ups of the twofold symmetric product of a general elliptic curve are non– empty and smooth of the expected dimension. This result, besides its intrinsic value, is an important preliminary step for the proof of nonemptiness of Severi varieties on general Enriques surfaces in [7].

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