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

Ciro Ciliberto, Thomas Dedieu, Concettina Galati and Andreas Leopold Knutsen

Mathematische Nachrichten, 2023, vol. 296, issue 2, 574-587

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 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.

Date: 2023
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https://doi.org/10.1002/mana.202100587

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