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arXiv · 2109.10735

Nonemptiness of Severi varieties on Enriques surfaces

Ciro Ciliberto·Thomas Dedieu·Concettina Galati·Andreas Leopold Knutsen
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Abstract

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

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Ciro Ciliberto, Thomas Dedieu, Concettina Galati, Andreas Leopold Knutsen. 2021-09-22. Nonemptiness of Severi varieties on Enriques surfaces. https://doi.org/10.1017/fms.2023.47

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