Abstract
Let X be a smooth projective surface and \(L\in \mathrm {Pic}(X)\). We prove that if L is \((2k-1)\)-spanned, then the set \({\tilde{V}}_k(L)\) of all nodal and irreducible \(D\in |L|\) with exactly k nodes is irreducible. The set \({\tilde{V}}_k(L)\) is an open subset of a Severi variety of |L|, the full Severi variety parametrizing all integral \(D\in |L|\) with geometric genus \(g(L)-k\).
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The author was partially supported by MIUR and GNSAGA of INdAM (Italy).
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Ballico, E. On the irreducibility of the Severi variety of nodal curves in a smooth surface. Arch. Math. 113, 483–487 (2019). https://doi.org/10.1007/s00013-019-01349-y
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DOI: https://doi.org/10.1007/s00013-019-01349-y