Severi varieties on blow-ups of the symmetric square of an elliptic curve
Journal article, Peer reviewed
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Original versionMathematische Nachrichten. 2023, 296 (2), 574-587. 10.1002/mana.202100587
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 nonempty 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.