Geodesic
Nonemptiness of severi varieties on enriques surfaces
Forum of Mathematics, Sigma, Tome 11 (2023)

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Let $(S,L)$ be a general polarised Enriques surface, with L not numerically 2-divisible. We prove the existence of regular components of all Severi varieties of irreducible nodal curves in the linear system $|L|$, that is, for any number of nodes $\delta =0, \ldots , p_a(L)-1$. 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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     author = {Ciro Ciliberto and Thomas Dedieu and Concettina Galati and Andreas Leopold Knutsen},
     title = {Nonemptiness of severi varieties on enriques surfaces},
     journal = {Forum of Mathematics, Sigma},
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     year = {2023},
     doi = {10.1017/fms.2023.47},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.47/}
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Ciro Ciliberto; Thomas Dedieu; Concettina Galati; Andreas Leopold Knutsen. Nonemptiness of severi varieties on enriques surfaces. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.47

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