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
2023-01-01
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.File in questo prodotto:
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