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.

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

Ciro Ciliberto;Thomas Dedieu;Concettina Galati
;
Andreas Leopold Knutsen
2023-01-01

Abstract

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.
2023
Severi varieties, nodal curves, degenerations, elliptic ruled surfaces
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/330196
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