Let $(S,L)$ be a general polarized Enriques surface, with $L$ not numerically2-divisible. We prove the existence of regular components of all Severivarieties of irreducible $delta$-nodal curves in the linear system $|L|$, with$0leq deltaleq p_a(L)-1$. This solves a classical open problem and gives apositive answer to a recent conjecture of Pandharipande--Schmitt, under theadditional condition of non-2-divisibility.

Nonemptiness of Severi varieties on Enriques surfaces

Ciro Ciliberto;Thomas Dedieu;Concettina Galati;Andreas Leopold Knutsen
2021

Abstract

Let $(S,L)$ be a general polarized Enriques surface, with $L$ not numerically2-divisible. We prove the existence of regular components of all Severivarieties of irreducible $delta$-nodal curves in the linear system $|L|$, with$0leq deltaleq p_a(L)-1$. This solves a classical open problem and gives apositive answer to a recent conjecture of Pandharipande--Schmitt, under theadditional condition of non-2-divisibility.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11770/336646
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